2. ~j--I-'II

IN o EDU:?: 0

I

KO'NRAD BASLER

BUNC-TSENC YEN ·

JO'HN A. MUELLER

BRUNO THURLIMANN

VVELDED P TE GIRDERS

REP RT NO. 251~ 11

I

OVERALL INTRODUCTIO'N AND

PART 1: THE TEST CIRDERS

--~~~.------------- ._-------_._----- --------

L\~~\i\i\lI\\1\~I~~\~~\ii~\\~\i[\~\ili\'\~i3 9151 00897581 1

Welded plate Girders, Report No. 251-11

submitted to theWelded Plate Girder Project Committee

for approval as a publication

WEB BUCKLING TESTS ON WELDEDPLATE GIRDERS

including

Foreword, Acknowledgement, Table of Contents,Nomenclature, Literature Survey and References,

Part 1: The Test Girders

by

Basler, K., Yen, B.T., Mueller, J.A.) and ThUrlimann, B.

Fritz Engineering LaboratoryLehigh University

Bethlehem, pennsylvaniaMay 1960

-lm=

FOREWORD

An extensive experimental and theoretical investigation

was carried out at Lehigh University with the purpose of

determining the carrying capacity of plate girders whose web

slenderness ratios were beyond the limits stipulated by

present specifications. While the theoretical study will

soon appear in the Proceedings of the ASeE, a complete

report on the experimen~al work will be published in this

Journal in four parts:

Part 1: IfThe Test Girders"

Part 2: "Tests on Plate Girders Subjected to Bending"

Part 3: flTests, on plate Girders Subjected to Shear"

Part 4: "Tests on plate Girders Subjected toCombi~ed Bending and Shearo "

The objective of this investigation was to determine

the postbuckling strength of thin web plate girders. The

design of transversely stiffened plate girders presently is

limited to girders whose web depth to web thickness ratios

do not exceed the value of 170. This limit was derived

from the web buckling theory 0 But in discussing the appli-

cation of the theoretical buckling formulae, Ref. 253, po 415,

Timo~henko suggests using a Jfactor of safety of only 1$5

-2-

against web buckling, since this occurrence does not cause

immediate failure of the girder. Also, similar consider­

ations are advanced by many foreign plate girder specifi­

cations to justify their factors of safety against web

buckling. For instance, the German specifications, Ref. 52,

require no more than 1.35 or 1.25 as a factor of safety

under principal loading, and principal and secondary loading

respectively. The corresponding Swiss specifications

recommend values of 1.3, 1.5, and 1.8 for plate girders used

in buildings, highway bridges, and railroad bridges respec­

tively. In Belgium~ Massonnet suggests a factor of $afey of

1.35 against buckling due to shear and 1.15 against buckling

due to bending, Ref. 162, p. 81. Thus, not only the safety

factors differ but they also seem to depend on loading

conditions and other factors. In order to clarify this

uncertainty, this plate Girder Project was started.

Sponsored jointly by the American Institute of Steel

Construction, the u.s. Department of Commerce Bureau of

Public Roads, the pennsylvania Department of Highways, and

the Welding. Research Council, the research project at

Lehigh University was guided by its I1Welded p·late Girder

Committee" whose members were:

-3-

E. L."Erickson, u.s. Bureau of Public Roads, Chairman

A. Amirikian, Bureau of Yards and Docks, U.S. Navy

L. S. Beedle, Lehigh university

Karl de Vries, Bethlehem Steel Company

F. H. i.D:f-ll, American Bridge Div., U.S. Steel Corp.

Neil van Eenam, UeS. Bureau of Public Roads

E. R. Estes, American Institute of Steel Construction

LaMotte Grover, Air ,Reduction Sales Company

T,. R. Higgins, American Institute of Steel Construction

W. H. Jameson, Bethlehem Steel Company

C. D. Jensen, pennsylvania Department of Highways

Knut Jensen, pennsylvania Department of Highways

Bruce G. Johnston, University of Michigan

K. H. Koopman, welding Research Council, Secretary

George W. Lamb,

w. B. McLean,

N. w. Morgan,

w. H. Munse,

Eo J. Ruble,

J. E. South,

R. M. Stuchell,

Bruno ThUrlimann,

George Winter,

W. Spraragen,

Consulting Bridge and Struct. Engr. (deceased)

Dravo Corpo~ation

DoS. Bureau of Public Roads

University of Illinois

Association of American Railroads

pennsylvania Railroad Company

Pittsburgh-Des Moines Steel Company

Federal lost. of Technology, Switzerland

Cornell University

welding Research Council

-4-

ACKNOWLEDGEMENTS

This investigation has been carried out at Fritz

Engineering Laboratory of Lehigh University, Bethlehem,

pennsylvania. Wm. J. Eney is Director of the Laboratory

and Head of the Civil Engineering Department. The chairman

of the Structural Metals Division is Lynn S. Beedle. Thanks

are due to both for the support which they have given to

this plate girder investigation.

T~e project is jointly sponsored by the American

Institute of Steel Construction, the pennsylvania Department

of Highways, the u.s. Department of Commerce Bureau of Public

Roads) and the welding Research Council. It is supervised

by the Welded plate ,Girder project Committee. The financial

support of the Sponsers and the continued interest and

gui.dance which the members of the Committee have given to

the project is gratefully acknowledged.

Sincere appreciation is expressed to the Engineering

and Weldment Department of the Bethlehem Steel Company and

in particular to Mr. K. de Vries for supervision and

faprication of the test girders. At Fritz Engineering

Laboratory, Ken Harpel and his staff of technicians built

-5-

the test rig and gave constant cooperation. Special thanks

are due to finer Taysi and Jin Tah for their assistance in

testing, data reduction, and in the preparat~on of the

figures; also to pete Cooper for proof reading the report.

Part 1:

Part 2:

-6-

Table of Contents

WEB BUCKLING TESTS ON WELDED PLATE GIRDERS

ForewordAcknowledgementTable of ContentsNomenclatureLiterature Survey and References

THE TEST GIRDERS

1.1 Introduction1.2 Girder Dimensions1.3 Steel properties1.4 Cross Sectional Constants1.5 Reference Moments and Loads1.6 Web Buckling Stresses1.7 Deflections

TESTS ON PLATE GIRDERS SUBJECTED TO BENDING

201 Introduction2.2 Design of Girders and Test Setup2.3 Basic Test Observations2.4 Ultimate Loads2.5 Failure Modes2.6 Discussion

·P-tQ)

~·H·~

C\Jr-f1

rlLf\C\J

·P-!<D.~

..H·lit

Part 3:

.Part 4:

-7-

TESTS ON PLATE GIRDERS SUBJECTED TO SHEAR

301 Introduction3.2 Design of Girders and Test Setup3.3 Ultimate Loads and Web Deflections3.4 SR-4 Strain Gage Measurements3.5 Additional Strain Measurements3.6 Discussion

TESTS ON PLATE GIRDERS SUBJECTED TOCOMBINED BENDING· AND SHEAR

4.1 Introduction4.2 Test Setup4.3 Test Results4.4 Discussion

-+

-8-

NOMENCLATURE

1. capital Letters - preferably used for quantitieswhich do not have linear dimensions

A Area of cross section

E Modulus of elasticity, 30,000 ksi

G Girder, used with a number, for example, G2 refersto girder Noo 2; also shear modulus, 11,530 ksi

I Moment of inertia

M Bending moment

NA Neutral axis

P Applied load

Q Statical moment of area

S Section modulus

T Test, used with a number, for example, TI refersto the first test on a girder

vX,Y,Z

Shear force

Cartesian coordinates (in inches) having theirorigin in the middle of the girder

~9-

2. Small Le~ters - preferably used for linear dimensions

a Panel length

b Web depth, b = 50" for all girders

c One-half the flange width

d Flange thickness

e : Distance from NA to the extreme fiber of the flange

h : .. Distance between the centroids of the flanges

k Buckling constant

1 Buckling length of a column

r Radius of gyration

t Web thickness

u,v,w Displacements in the X,Y,Z directions

x Longitudinal coordinate with origins at eitherend of a girder's span

3. Greek Letters - used for nondimensional parametersand stresses

a=a/b Aspect ratio, panel length to web depth

~=b/t Web slenderness ratio, web depth to web thickness

E : Strain

v Poisson's ratio (= O~3)

cr Normal stress

1: Shear stress

-10-

4. S~bscripts Examples

a Above Sa Section modulus above NA

b Below eb Distance from NA toextreme fiber of bottomflange

cr Critical ocr Critical normal st,ress

t Centerline v~ Centerline deflection

e · End Ie Moment of inertia of· end sections

f Flange Mf Moment contributed byflanges

i Ideal 'Lcri Ideal critical shearing,stress before inelasticreductions

m · Middle 1m Moment of inertia of· middle or test section'

n .. Neutral axis In Moment of inertia about· NA

p · plastic Pp Load causing the· plastic moment

u Ultimate Pu Ultimate load

v Combined aver Critical stress undercombined loading

w Web Aw Area of the web

y Yield ayw Yield stress of web

-11-

LITERATURE SURVEY AND REFERENCES

An extensive study of the pertinent literature

preceded the investigation. This study led to a survey

of literature on plate ~tability of plate girders. Although

this study was conducted in 1957, any additional references

appearing since then in the technical literature have been

inserted at their proper lo'cation. Figure 1 graphically

summarizes this survey, indicating place, time and 'nature

of the various papers.

This section contains first the abbreviations, as they

are found in the English, French, and German literature.

Then follows the literature survey, with a translation of the

title if in a foreign language. The references are listed

alphabetically by authors. Finally, some addit·ional

references, Ref. 269 to 276,complete this section & These

are papers to which referen~e· is made in this report but do

not necessarily belong in the literature survey which is

concerned with plate stability only.

Publications by:

Abbrevia,tionAbbreviation Full Title

Type of Their publications:

Meaning ofAbbreviation

Abbreviation

JO\Lrnals

Full Title

I.V.B.H.

A.l.P .. C.

I.A.B.S.E.

N.A.C.A"..

A.S.C.E.

Internationale Ver­einigung fUr Brllk­.kenbau und Hochbau

Association Inter­nationale des Pantsec Charpentes

International Asso­ciation for Bridgeand Structural"Engineering

N~tional AdvisaryCommittee o~ Aero­nautics

American Society ofCivil Engineers

Vorb.Schl.Ber ..Abh.

Publ.p"rel.

Rap. f.Mem.

Prel.Rep ..

F .. Rep ..Publ.

T.N.T.M.~v .. R.

Proc.Trans.

VarberichtSchlussberichtAbhandlungen

PublicationpreliminaireRapport finalMemoires

Preliminary·ReportFinal ReportPublication

Technical NoteTechnical Memor,\Tartime R~port

ProceedingsTransactions

Bauing..

Stahlbau

Ing~ ArchLy

J~ Aero. Sci.

Nat.Aero.Res.lnst.

Weld. & Met. Fabrn.

Der Bauingeni.eur

Der Stahlbau

Ingenieur Archiv

Journal of AeronauticalScience

National AeronauticalResearch Institute

Welding and Metal Fabrication

BJ-I[\)I

Inscicut f~r Bau­Inst.f.Baust. sta~ik an der Eid­a.d. E.T.H. genossischen Tech­

nischen HochschuleZ~rich

Mitt" Nr .. Mitteilung Nr~

Luft£ .. Forsch~

Z~Flugtechn.u.Motorluftsch.

Luftfahrt-Forschung

Zeitschrift ftir Flugtechnikund Motorluftschiffahrt

T.K.V.S.B.

Technische Kommis­sian des VerbandesSchweizerischerBrUckenbau- undStahlhochbauunter­nehmungen. Changed1956 into: Schwei­zer Stahlbauverband

Mitt. Nr. Mitteilung Nr.

z~angew.Math.u~Mech.11

Zeitschrift fur angewandteMathematik und Mechanik

LITERATURE SURVEY

1 .. Back;, G. and Schumann ~_ L.nStrength of Rec-tangular Flat plates Under EdgeCompressi9n"N.A .. C.A.~· Rep. No. 356, 1930.

2. Ballerstedt, w. und Wagner~ H.'Ueber Zugfelder in ursprUnglich gekrllmmten, dUnnenBlechen- bei Beanspruchung __durch -Schubkr¥~te'fLuftf. Forsch.~ _vol. 12, 1935., S. 70. -I

"On the Tension Fields of Initially CUrved, ThinSheets Under Shear"

3. Ban, S."Knickung der rechceckigen platten bei verHnderli­cher Randbelastung"I.V.B.H., Abh.~ Vol. 3, zUrich, 1935, S. 1.

"Buckling of Rectangular plates Under VariousLoading Conditions"

4. Barbre, R."Beulspannungen von Rechteckplatten mit I1ings­steifen bei gleichm~ssiger Druckbeanspruchung 'f

Bauing.~ Vol. 17, 1936, S. 268.

"Critical Stresses of Rectangular'Plates withLongitudinal Stiffeners Under Uniform Compression"Has been translated into English:Translation 78 of Navy Dept .. David Taylor ModelBasin, Washington~ D.C., 1943.

5. Barbre~.R..rtStabilitllt gleichmHssig gedrUckter Rechteckplattenmi.t LHngs- oder Quersteifen1l

Ing~ Arcbiv, Vo~. 8~ 1937, s. 1~7;

"The Stability of UnuQrinly Loaded RectangularPlates with Longitudinal or Transverse Stiffeners"Translated into English:

_ "N.A ... C.A:. ~ T.M. No. 904;, 1939.'

6. Barth~ W.~ BBrsch-supan~w. und Scheer~ J.. f~eu15icherheit ausgesteifter Ree~teekplattenbei

zusammengesetzter Beanspruchung fL

Stahlbau, Vol. 28~ 1959, S. 68.

"Safety Against Buckling of Stiffened RectangularPlates Subjected t.O Combined Loading Cases"

7 _ Basler, K."Strength of Plate Girders"Ph.Dc Dissertation~ Lehigh University~ Bethlehem~

pennsylvania~ October 1959.Reprints or Microfilms available through:Hie. 59-6958~ University Microfilms, Inc·. ~

313 N. First Street, Ann·Arbor~ Michigan.

8.. Basler, K. ~nd Thllr1imann, B."Plate Girder Researchlf

A.I.S.C. National Engineering Conference,Proceedings 1959, .American Institute of SteelConstruction, New York.

9 . Basler, K. and Thllrlimann , B."Buckling Tests on Plate Girders ff

International Association for Bridge and Struc­tural Engineering, preliminary Report, 6th Congress,Stockholm ~ 1960. . "

10. Batdorf, S.B."Theories of Plastic Buckling ll

J. Aero. Sci.~ Vol. 16~ No.8, 1954, p. 543

,f-'W

(

, j.

11" Bergmann~ St. und Reissner~ H. ."Ueber die Knickung vou'Wellblechstteifen bei

SchubbeanspruchUr.."'1.g iT

Z~ Flugtechn. u. Motorluftsch., Vo16 20, 1929,s. 475 und Vol .. 2.1 07 1930, 5 .. 306.

nan the Buckling. of Corrogated Panels Due to Shearn

17" Bijlaard, P .. P ..rtGrundlegende Betrachtungen zum Ausbeulen derPlatten und Sehaien im plastischen Bereich1f

lust .. f ... Baust6- a.a. R.T.H.:; Hitt. Nr" 21,Verlag Leemann, Zllrich, 1948.

ITFundamental Considerations on the Stability ofPlates and Shells in the Plast.i.c. Regionll

12. Bergmann, St.HUeber Schubknickung von isotropen und anisocropenPlattenU

3rd Int. Congr. for Applied Mechanics, Proe.,Vol. III, Stockholm, 1930, p. 82.

nOn the Bllckling of Isotropic and AnisotropicPlates Due to ShearTl

13. Bergmann, St. und Reissner, H."Ueber die Knickung von rechteckigen Platten beiSchubbeansprucnung 11

z. Flugtechn .. u. Motorluftsch., Vol.23, 1932, s. 6.

HOn the Buckling of Rectangula.r Plates Under ShearnGets k value for a = 2, under pure shear ..

14. Bergmann, St."Be~..avior-of Buckled Rectangular plates Under theAction of Shearing Forces"Institution of Structural Engineering and BridgeBuilding, Rep., Stockholm, 1948.

lS~ BLjlaard, P.P~

J~heory of Local Plastic Deformations ~ Theory ofthe Elastic Stability of Thin Plates Tt

I .. A B.S.E., Pub1 4 , Vol .. 6 y 1940-41, pp. 27-69.

16. Bijlaard, P .. P.nSome Contributions to the.Theory of Elastic andplastic StabilityUI.A.B.S .. E., Publ., Vol. 8, Zurich, 1947, pp. 17-80.

L8~ Bijlaard, P.P.tITheory and Tests on the Plastic Stability ofplates and Shells"J. Aero. Sci., Vol. 16, No. 9~ 1949, pp. 529-54l~

19 .. Bij1aard, P.P., Kollbrunner, CoOF .. und Stussi, F"ttTheorie und Versuche tiber das plastische Ausbeu­len von Rechteckplatten unter gleichmassig ver­teiltem LangsdruckJf

I V.B .. H., Vorb., 3. Kongress, Luttich, 1948,8.119 ..

"Theory and Experiment.s on the: Plastic Buckling ofRectangl..11ar plates Under Uniform Compre~sionlf

20~ Bleich, F .."Die Stabilitat dlinner l-Jartde gedrUckter Stl{be fT

I.V .. B.li .. , Vorbe, 1. Kongress, Paris, 1932~ s. 130.

"The Stability of Thin Halls in Compression Members f'

21. Bleich, F.tTBuckling Strength of Metal Structures" (Book)McGraw-Hill Company, New York, London, andToronto, 1952.

22. Boley, B."The Shearing Rigidity of Buckled Sheet Panels"J. Aero. Sci., Vol. 17, No~ 6, 1950~

!----2i-­-t-

~

, 2~" .Bollenrath, F""Ausbeulerscheinungen an ebenen,_ auf Schuh bean-spruchten Platten" '.Luftf" Forsch., Vol ~ 6~ 1929, S':> _1, (auch ThesisTechn. Hochschufe, Aachen" 1928) ,,'7

"Buckling Phenom~na on Flat plates Subjected toShear l

'

24. Bornscheuer j F .. W' " ,,'1~indeststeifigkeiten von Plattenaussteifungenbei berUcksichtigter Verdrehsteifigkeit"MAN-Forschungs-Heft, 1 .. Halbjahr, 1952.

'~he Optimum Rigidity of Plate Stiffeners Takinginto Consideration Their Torsional Rigidityfl

25". Brci~, V"''Ueber versteifungen einer auf Schub beanspruchtenrechteckigen Platte 11

Stahlbau, Vol. 25~ .1956, S. 88.

"On the Stiffener Rigidity of a Rectangular PlateUnder Shearn

-·26. Bridget, F.J .. , Jerome, C C .. , andVoseller, A"B."Some New Experiments on Buckling of ThinwallConstructions"A.S.M .. E., Trans., Vol. 56,1934, p" 569.

27 • Bryan, G"H.nOn the Stability of a plane Plate Under Thrustsin Its Own Plane, With Applications to theBuckling of the Sides of a Ship" ~

Math." Soc .. , Proc", Vol .. 22j1 London, l891~ p. 54-.

28.. Bryan~ G"R""On the Buck1ing and Wrink~ing of Plating whenSupported on Parallel~ Ribs or on a RectangularFramework"Math. Soc., proc ... ~ Vol" 25, London, 1894, p. 141.

29'~ Budiansky, B. and Connor:p- R ...W~

. . "Buckling Stresses· of Clamped Rectangular' ·FlatPlates in'Shear"N.A.C ..A.·'- T~N •. 15S·g., 1948.

30. Budiansky; B", Connor, R~W"., and, Stein, M' .."Buckling in Shear' of Continuous Flat Plates"N"A ...C.A~, T~N~ 1565, 1948"

31.. Budiansky, B. and Hu, P .. C.."The Lagrangian Multiplier Method of FindingUpper-and Lower Limits to Critical Stresses­of Clamped Plat-esrlN.A:C"A", T.N" 848, 1946"

-3'2. Budi.aIi.s1<y, -Be-, Hu,. P ,,'C.• , andConnor,.R .. t-f..''Notes on the Lagrangian· Multiplier .Method 'inElastic Stability- Analysi.s tl

N.A.C"A", T·~N .. 1558~ 1947,,-

33n Budiansky, B. and Seide, P."Compressive Buckling, of Simply Supported 'Plateswith Transverse Stiffeners" -N..A..C ...A., T.N. 1557., 1948~

34. Burchard, W."Beulspannungen~der quadratischen Platte mitSchrHgsteife under Druck bz.w.~ Schuh"Dig. ~~chi.v, Vole- ~8-, 1.937, SO. 332.

"Buckling of a Square plate With a DiagonalStiffener Under Compression or Shear"

35.. Chapman, J.C ..."Behavior in' Pure· Bending of Box Gi.rders"Engineer, 1954, pp. 198 (514), 252~ 253-257"

Ij--J

\Jl.I

36.. Chapman, J .. c .. and Sparkes, S.R .."Structural Investigation on Box--Girders"Brit .. Shipbldo- Res .. Assn .. , Part i &~2,

Report Nos. 122, 127, and 160 ..

37 .. Chwalla, E."Das allgemeine StabilitHtsproblem der gedrUckten,-durch.Randwinkel verstHrkten Platte"lng. Archiv, Vol. 5, 1934, s. 54.

r~he General Stability Problem of a plate Rein­forced by'Angles Along rts Edges"

38. Chwalla, E."Die Beme-ssung --der waagrecht ausgeste±ften -Steg­bleche vollwandJ..ger Trager"I.V.B.H., Vorb., 2. Kongress;, Berlin-MUnchen,1936, S .. 957.

HThe Design of Longitudinally Stiffened Webs ofplate Girders 'I

39Q Chwalla 7 E."Beitrag Lur 'StabilitHtstheorie des Stegblechesvollwandiger TrMger"Stah1bau, Vol .. 9;, 1936;, ~. 161.

"Contribution to the Buckling Theory of Webs ofPlat~__ Gi-rder fl

Solves the case of a longitudinally stiffenedplate under pure bending.

40. Chwalla;, E."Die Bemessung des Stegbleches im Endfeld vo11wan­diger Trager"Bauing., Vol. 17, 1936, s. 81.

'~he Design of a Web Located in the End Panel of aPlate Girder ll

41. Chwa11a, E .."ueber die probleme und L8sungen der StaQil~tHts­

theorie des Stahlbaus Jt

Stahlbau, 1939, S. 1.

"On the probJems and solutions of the Stability_of Steel Structures"

42~ Chwalla, E.flErlHuterungen zu den Knick- und Beulvorschrift-enfiir Baustahl, DIN E 4114, 1940 ft

Erganzung ~ur Bautechnik, Vol". 17, 1939;, Nr. 51/52und Vol. 18;, 1940;, Nr. 2/3.

nExp1~nations to the Buckling Specifications forSt-ructural-Steel"

43. Chwalla, E.'TIeber die Biegebeulung der IMngsversteiftenPlatten und ~sproblem der Mindeststei£igkeit T1

Stahlbau;, Nr. 18/20, 1944, s. 84.

"On the Buckling Problem of a LongitudinallyStiffened Place Under Bending Moments and theProblem of Optimum Stiffness"

44. Chwalla;, E."Aussprache und Vortrag anlasslich der Ehrenpromo~ion

an der Techn. UniversitMt Berlin-Charlottenburg"Stahlbau-Abh .. , Heft 3, KBln, 1954.

J'Lecture of -the Technical University Berlin on theoccasion of His Promotion to a- Honorary Ph.D. Degree1f

45. Chwalla;, E. und Novak, A.tlTheorie der einseitig angeordneten Stegblechsteife"Stahlbau, Vol. 10, 1937, s. 72 und 92, oderBauing.;, Vol. 10;, 1937.

rtTheory of Unsymmetric web Stiffeners"

If-.I0'I

46. Coan, J.M."Large Deflect~on Th~ory for, Plates with SmallInitial Curvature, Loaded in Edge Compression"Jour .. Applied Mechanics,- Vol. 18, No.2, June 1957 ..

47. Cornfield, G..M-. and Sparkes, S.R."Buckling of t;he Webs of Plate Girders" .Jour .. of -the Inst.,_of Civ .. Eng .. , Vol.24, 1945, p.59.

48. Cox, H.L.lIsummary of the Present State of Knowledge RegardingSheet-Metal Construction"Aerori.Res.Comm.Rep .. and Mem .. , No .. 1553; London, 1933 ..

49.. Cox, H.L.fTBuckling of Thin-Plates in Compressionn

Aeron .. Res.Comm.Rep. and Mem., No .. 1554, London, 1933.

50. Cox, H.L .. and Gough, H.. J .."Some Tests on the Stability of Thin-Strip MaterialUnder SJ:1.earing Forces in the Plane of the StripllRoy. Soc .. , Froe .. , Ser .. A, Vol. 137, London, 1932,p. 145.

53. Deutscher Normenausschuss und Deutscher StahlbauverbandTlErlHuterungen zur Begrl:lndung des.Normblattent­wurfes"Beuth-Vertrieb G.m.b ..H.. , Berlin W 15 und K8ln~

S .. 6-18 ..

"Commentary on the Provisions of the Standar4Specificat.ion$"Gives an excellentexplanatiop. of the. German"Specif~cations by E .. Chwalla.

54. j Deutscher StahlbauverbandI r'Stahlbau"

Stahlba~-VerIags-G.. m.. b .. H., KBln,· Banc;i 1, 1956.

ltSteel -Struc tures'" (B-ook)

55. Donnell, L.H .. , Karman, T.H., and Se<:;hler, E .. E.TfStrength of Thin Plates in Compression"A.S.M.E .. , T~ans., Vol. 54, 1932, p. 53.

56.. Drucker) D.C: and Onat, E ..T.aOn the Concept of Stability of Inelastic sys-tems"J. Aero .. SGi., Vol. 21, No. &> 1954, p. 543 ..

I......-..]I

.51 ..

52.

nenke, P.H.·1JAnalysis and Des~gn of Stiffened Sheart...rebs 1T

J", Aero ... Sci-., -Vol. 17, 1950 ~ p. 217 ..

Deutscher Normenausschuss"DIN 4114, Blatt 1 und 2 ft

Beuth-Vertrieb G.m'.b.H., Berlin W 15 und KHln,1952 una 1953.

l~he-German Standard Specifications CoveringScability Problems in Steel Structures: ColumnBuckling, Lateral Buckling, and Plate· Bucklingff

part 1 contains the specifications, Part 2 givesaddLtional recommendations.

?7 .

58.

Dubas, Ch ..rrContribution a l'etude du voilement des tolesradiesn

A.I.P.C .. , Publ .. prel .. , 3e congr .. Liege, 1948 etlnst .. f .. Baust .. a.d. E.T.H., Mitt. Hr. 23,Verlag LeemaDn', ZUrich, 1949.

IlContrihutions to the Problem of Buckling ofStiffened Pl~tesn

Derives locati.on of- most efficient longitudinalstiffener ..

Erickson~ E ..L.. and van Eenam;) N.ttApplication and Development of A.A.S.H.O.Specifications to Bridge Design" .A.S~C.E ~ Froe., Vol. 83) ~957, p. 1320-10/12.

61. Falconer, B.H. and Chapman, J.C."Compressive Buckling of Stiffened Plates lt

Engineer, Vol. 195,. 1953, pp. 789, 882.

59.

60 ..

62.

Fairbairn, w."Conway and Britannia Tubular Bridges ll

184-9

Falconer,- B.H."Post Buckling Behaviour of Long Square BoxesUnder Torsion fr

Engineer, Vol. 196, 1953, p. 690.

Faxen, O.H.'rnie Knickfestigkeit rechteckiger PlattenH

z. angew. Math. u. Mech., Vol. 15, 1935, S. 268.

-'The Buckling 'Strength of Rectangular Plates fT

66.

67..

_08 ..

Friedrichs,. K.O. and Stoker,. J.J.- "Buckling of the Circular .. Plate Beyond the

critl-cal Thrust" >

Jour. of Applied Mechanics, March 1942, p".. A7 __

Frbhlich-,. H.nStabilitHt der gleichmassig gedrtickten·Recht­eckplatte mit Steifenkreuz 1J

Thesis Tech. Hochschule Hannover, 1937 undBauing., Vol. 18, 1937, S .. 673.

i1Stability of uniformly Compressed RectangularPlate with Crossing Stiffeners ' !

Gaber, ~.

"Beulversuche an Modelltragern aus Stahl I'Bautechnik, Vol .. 22, 1944, s. 6.

"Buckling Tests~_on Model Girders in Steel'f

63. Federhofer, K.l'TragfMhigkeit der tiber die Beulgrenze belastetenKreisplatte n

Forsch. auf d. Gebiet d. Ingenieurwesens> Vol. 11,1940, s. 97.

f1Tne Ultimate Load of the Circular plate LoadedBeyond BuckliQgrr

64. Fienup, K.L., Levy, s.> and walley, R.M.'lAnalysis of Square Shear Web Above Buckling LoadtT

N.A.C.A.·, T.N ... 962, 1945.

65.- Friedrichs, K.O .. and Stoker, J .. J.ffThe Non-Linear Boundary Value Problem of theBuckled Plate tT

Nat".. Acad .. of Sciences, Proc .. > Vol .. 25, 1939,p .. 535.

69. Gaber, E.1tUeber die Aussteifung von Vollwandtr~gern ausStahlTf •

Stahlbau, Heft 1 und 2, 1944.

nOn the Stiffening of Plate Girders t1

70 . Gall, H. ~7 .."Compressive Strength of Stiffened Sheet panels'TReporeed by Newell> J.S. ItStrength of AluminumAlloy Sheets q

, Airway Age, 1930.

71. _Gerard, G. .l'Secant Modulus Method for Determining plateInstability Above the proportional Limit fT

J. Aero. Sci., Vol .. 13, 1946, p. 38.

II--'CDI

72. Gerard~' G."Critical Shear Stress of Pl.ates Above theProportional Limit1f

Jour. of Applied Mechanics, Vol. 15 ~ No. l"1948~ pp. 7-12.

73. Gerard~ G. and Becker" H."Handbook of Structural Stability J1

N.A.C.A.;r T.N. 3781 to 3785~ 1957.

74. Girkmann~ K~

f'FIMchentragwerke t!

Springer~ Wien, 1956.

JlTheory of Disks~ Plates, and ShellsH (Book)

75.. Godfrey, H.J. and Lyse, I.-:Investigation of fNeb Buckling in Steel Beams lf

A.S.C.E., 'Trans.~ Vol. lOO~ 1935~ p. 675.

76. Green, G.G.~ Winter, G., and Cuykendall, T .. R.'fLight Gage Steel Columns in Wall-&aced panels rf

Cornell Univ. Engng. Exp. Station Bull. No. 35,Part 2, 1947.

77. Greenman, s. and,Levy, s."Bending \flith Large Deflection of ClampedRect~ular Plate with -Lengtl1.-_Width Ratioof 1.5 Under Normal Pressur~1I

N.A.C.A.~ T.N. 853, 1942.

78. Hampl~ M.TJEin B~itrag ~ur Stabilitat des horizontalangesteiften Stegbleches' f

Stahlbau) Vol. lO~ 1937) s. 16 und 21.

UA Contribution to the Stability of LongitudinallyStiffened Web PlatesU .

19. Hartmann;r F."Knickung - Kippung - BeulungTJ

Leip4ig und Wien~ 1937" VIII Absatz ..

"Column Buckling - Lateral and Plate-Buckling"(Book)

80. Hartmann~ F."StahlbrUckenIJ

herausgegeben von E. Melan, Wien~ 1953 ..

"Bridges in Steel'l (Book)

81. Hec·k, O.S. and Ebner~ H."Methods and Formulas for calculating theStrength of Plate and Shell Structures asu'sed in Aircraft DesignTJN.A.C.A.~ T.M. 785~ 1936.

82. Heimerl, G.J~

ItDetermination of Plate Compressive Strength"N.A.C.A., T.N. 1480~ 1947.

83. Heyman, J. and Du·tton, V.L."Plastic Design of plate Girders ~>Jith UnstiffenedWebs"Weld. & Met. Fab.~ Vol. 22, July 1954, p. 265.

84. -Hill, H.N.;"Chart for Critical Compressive Stress of FlatRectangular plates 1f

-

N.A.C.A.~ T.N. 773, 1940.

85. Hoff, N.J.~fNote on Inelastic Buckling lT

J. Aero. sci., Vol. 11, 1944~ p. 163.

It-''-D

I

86. Hoff, N.J., Boley, B.A. 3 and Coan, J.MoIf The Development of a Techniqu~ for Tes,tingStiff Panels in Edgewise Compression tl

Soc. of Exp. Stress Analysis, Proc., Vol. 5,No.2, 1948, pp. 14-24.

87. Hotchkiss, J.G."New Ways to Cut Bridge weight Lead to RecordSpans"Engineer~g News-Record, Nov. 7, 1957, pp. 36-51.

Gives some excellent examples on German plateg'irder bridges.

:0808. -'"11oUbo1t, J.C. and Stowell, E.2."Critical Stress ,of, Plate Columns l1

N.A.C .A.) T .,N. 2163, 1950 ..

89. Houbotte, M."Versuche {{her die 'Festigkeit blecherner TrllgerH

Der Civilingenieur,. Vol. 4:1 18;5'8, S. 98.

tfTests on the Strength of Plate, Girders lt

90. Hu, p.e.) Lundquist, E.E., a;nd Batdorf, S .. B.rTEffect pi Small Deviations from Flatness on theEffective Width .and,Buckl.ing ,o.f Plat.-es in

"Compres SiOn-~l

N.A~C.A.. , T.N. 1124, 1946.

91. Iguchi, S ..I1Allgemeine L8sung der Knickaufgabe fur recht­eckige Platten"lng. Archiv, Vol. 7, 1936, S. 207.

"General Solution for the Buckling Problem of thctRectangular Platen

9-2. Iguchi., -5 •- "Die Knickung der rechteckigen.Plattedurch

SchubkrH.ft~n

lng. Archiv, Vol. 9,' 1938, 5.''1-12.

T1Buckl.ing of RectangUlar Plate Due to Shear"

'3. Ilyushin, A.A.TtThe EJ.asto-plastic Stability of P1ateslf

N.A.C'.A'., T.M. 1188., Dec. 1947.

94.. Johnson, 'J.H. and Noel"R.G.f'Critical Buckling' -Stress for. Flat' RectangularPlates' -Supporte"d-:Along All--Edges and ElasticallyRestrained Against Rotation Along the UnloadedCompression Edge'~,

J. Aero. Sci., Vol. 20, No.8, 1953" pp. 535-540.

95. Karman von, Th."EPcyklopHdie der Mathematisclien Wissenschaftenn

Vol. 15/4, 1910, S. 34~.

Derived the 'differential equations for the platewLth 'large deflect~ons.

96. Karman vori, Th .. , sechler, E .. E .. , and Donnell,. L.H.J~he Strength of Thin. Plate ' in -.Compre'ssion,t.A.S.M.E., Trans. 54, 1932. '

97. Kaufmann, W'.i1ueber ·unelastisches Knicken rechteckiger Platten"Ing. Archiv, Vol. 7, 1936, s. 156.

"On Inelastic~Buckling of Rectangular Plates"

98 ... Kerensky, O.A., Flint, A.,R., and~own', W.Ch.''The Basi.s for Dengn of Beams and plate Girders"in the 'Revi.sedBritish Standard 153 rt

The Insti.tution o£.Ci.vi.l Engineers, Great GeorgeStreet, westminster,. London S.W.l~ Struct. paperNo. 48~1956, pp. 427-440. ,

If\)oI

99-.,. KIBppel, K.IIZur EinftIhrung derneuen. StabilitHts-Vorschriften rT

Stahlbau-Abh., Heft 12, 1952!i S... 92 ..

11commentary to the New German Standard Specifi­cations"

100~ Kloppel, K. und Lie, K.H."Das hinreichende Kriteriwn ftir den Verzweiguugs-·punkt des elastischen Gleichgewichts"Stahlbau, 1943, S. 17.

'~he Sufficient Criterion for the Point of Bifur­cation of the Elastic Equi1ibrium"

101 .. KlHppel, K. und Scheer, J."Das praktische Aufstellen von Beuldeterminantenfur Rechteckplatten mit randparallelen Steifenbei Navierschen Randb~dingungen"-

Stahlbau, Vol. 25, 19s6~ s. 117.

"The Derivation of Buckling Determinants ofRectangUlar Plate~ ~o1ith Stiffeners" the plateBeing Simply Supported and the. StiffenersParallel to the_ Edges U

1.02..Kloppel, K. und Scheer, J.'1Beulwerte del:' durcb. ",wei_gleic~e LMngssteifen inden Drittelspunkten der Feldbreite ausgesteiftenRechteckplatte bei Navierschen Randbedingungen l

,'

Stahlbau!iNr. 11', 1956, s . .265/7.4 und Stahlbau,Nr. 9, 1957, S. 246/52.

IrBuckl-ing Values of ·a Simply Supported RectangularPlate with Two Lungitudinal Stiffeners Subdividingthe Panel into Three Equal parts"

103. K18ppel, K. und Scheer, J."Beulwerte der durch eine rllngssteife im Drittels­punkt der Fel~breite ausgesteiftenRechteckplattebei Navierschen Randbedingungen" -Stahlbau,~Vol. 26, 1957, S. 364.

'1Buckling Values of a Simply Supported RectangularPlate with One Longitudinal Stiffener Located atthe Third-point. of the panel Depth"

104. Kl8ppel, K. und Scheer, J."Beulwerte der durch eine LJ:lngssteife im Viertels­punkt der Feldbreite ausgesteiften Rechteckplattebei Navierschen Randbedingungen TT

Stahlbau, Vol. 27, 1958-, S .. 206.

"Buckling_Values of a Simply Supported RectangularPlate with One Longitudinal Stiffener Located atthe Quarter-point of the panel Depth"

105. Knipp, G._. 'HUeber die Stabilitlit der gleichmHssig ged~cktenRechteckplatte mit Steifenrost~J -Bauing., Vol. 22,1941, 'S. 257.

110n the Stability of the Uniformly CompressedRectangular Plate Stiffened by a GrillageSystem"

106. Kollbrunner, C.F.>'Das Ausbeulen des auf Druck beanspruchtenfreis tehenden r.vinkels:TInst. f. Ba~st. a.d. E.T.H.:J Mitt. Nr. 4,verlag Lee~ann, .Zllrich, 1935.

~ "Th'e Buckling of Compre~ssed Angles"About 500 steel and aluminum'alloy angles weretested. The author used angles for his teststo simulate buckling of plates being simply.supported along one edge and free along the other.

If\)J--II

107 .. " Kollbrunner, C.F.. _"IfStabilitHt der auf Druck lieanspruchten plattenim elastischen urid plastischen·Bereichl1

'. Jf.I.V.B.H., Abh .. , Band 7, verlag Leemann, Zurich,1943/44, S. 215. -

111..- Kollbrunner,. C.F. mid Herrmanri., G.t'El-astischeBeulung von" auf .einseitigen" 'unglei.ch-mH'ssigen Druckbeanspruehten Plattenll

•

T.K .. V .. S.B., MLtt_ Nr. 1, verlag Leemann, zUrich,1948.. .

'-rhe 'Stability of Compressed Plates in the. Elastic·and Inelastic Region"Experimental Investigation ..

"Elastic Stability of Non~Uniformiy CompressedPlates tr

-

108. Kollbrunner,- C .. F .."Das Ausbeulen der auf einseitig.en, gleichmHssigverteilten Druck beanspruchten Platten 1melastischen _und plastischen _Bereich"In~t .. f .. Baust .. a.d. E.T .. H., Mitt... · Nr. 17,verlag .Leemann ,. Z&ich, 1946.

''l'he Buckling of Uniformly Compressed Plates inthe· Elastic and Inelastic Rangeff

Experimental Investigation .. ,

109. Kollbrunner,C .. F.. "Versuche {{ber das Ausbeulen- von Rechteckplatten

unter dreieckf8rmig vertei1tem Ilngsdruckrf

I.V .. B.H .. , Schl'OBer.) 3. Kongress, LHttich, 1948,s. 301 ..

112.. Kollbrunner,. C ..Y. und Hen:m-ann~ G."Reine Biegungsbeulung rechteckiger Platten ime1astischen Bereichfl

T.K.V ..S .. B .. , Mitt. Nr .. 2, verlag Leemann,. ZHrich,1949.. -

t'Elastic Stabili.tY of- Rectangular Plates underPure Bending'J

113. Ko1lbrunner, C .. F. und Herrmann, G."Der Einfluss der" Poi.ss-on" schen Zah1 auf die Stab:L­litHt rechteckiger ,'PlattenU

T .. K.V.S.B., Mitt. Nr. 4, verlag Leemann, zllri.c~,­1951.

''The Influence of Poisson's Rati.o on the ·Stabilityof Rectangular~PlatesH

If\)f\)I

/y/

"The Influence of Shear on the Stabili.ty of Plat.esin the Elastic Rangeff

Usually, the shear distributionover the thickness of the plateis neglected· in calculating thestrain energy. The authors showthat this simplification gener­ally results in a negligibleerror.. Note that the publ~ca-

t:ion dea1s o~ -t:xz and ·";yz> noton 1:xy

114 ~ . Kollbrunner, C.F ~ und Herrmann,. G'O"Einfluss des Schubes auf cl:Le' S-tabi.LLtlit der' Plattenim elastischen Bereich"T.K.V .. S.B., Mitt .. Nr. 14,. Verlag VSB, ZHri.ch,1956 ..

"Buckling 'Tests of Rectangular plates UnderCompression with Triangular Distribution"

''The Stability of Plates in the plastic Range"The theory of A.A. Ilyushin is compared withtest results. .

110.. Kollbrunner, C .. F. und Herrmann, G.. .-IJStabilitHt der Platten im p1astischen Bereichu

Inst .. f .. Baust. a.d .. E .. T.H., Mitt. Nr .. 20,.Verlag Leemann, Zllrich, 1947 ..

115 • - Kollbruniler, C..F.. und Hernnann, G... ."plattenbeulung-im plastischen-Bereich mitBerUcksich.tigung der Schubverzerrungt'T.K.V'.S-~B ... , Mit-t. Nr. 19, verlag VSB,Zllrich, 1959~ -

'~late Buckltng.in the plastic Range byConsidering Shear H

As in the previous re£er~nce, shear refersto.'t XL and 't yz.' not 't xy.

116 ..Kol1brunner, C.F. und Meister, M.'IAusbeulen1

' (Book)Springer-ve~lagBerlin, GSttingen und He1delberg.

_~te ,.Buck] jog"

117. Kondo~ K. and yamamoto,' M. __11Buckling and- Failure of Thin Rec"tangular platesin Co~pression" .Aeron. Res. lnst.,. Rep .. No. 119,. Tokyo, Imp._ Univ.,.1935.

118. Krabbe, F.W."Beitrag ~ur Berechnung der Stegblechaussteifungenvol+wandiger B1echtrager 1f

Stahlbau, Vol. lO~ 1937, s. 65.

"Contribution - to the calcu1~_t.ion of Web Stiffenersof Plate Girders"

119. Krabbe, F.W.o~rundsHtzliche"BemerkungenLur Frage der Beul­sicherhei-t der Stegbleche vollwandiger Blechtrlig.er n

. Stahlba~, Vol. 10, 1937, SO. 97.

"Fundamental Considerations on the Problem ofBuckling safety of plate Girders"

12.0. Kroll', W.D. "TlTables of Stiffness and carry-Over Factor forFlat Rectangular Plates-Under Compressionn

N ..A. C.A., W...R. t.-39-8" 1943.. "

121. Kroll, tV.D., Fisher, G.P .. ," and Heimerl., G..J.TtCharts for Calculati..on_of -the Cri.tical"Stressfor Local InstabilitY of Columns wLth r-, Z-,Channel-, and _Rectangular-Tube SectionsTl

N ..A.C.A .. ,W..R .. L~42?, 1943.

122_. Kromm,. A.tlZur Frage der Mindests~eifigkei.tenvon rlattec..-aussteifungenTl .

Stahlbau,. Heft 18/20,. 1944, S ... 8l-84"~

nOn- the prob-lem of Optimum Rigidi_ty of Sti£fenedPlates"Contains fundamental- considerat:lons .. -

123. Kromm., AoO und Marguerre, K.I1Verhalten eines von S_chub-. und DruckkrHften be..an­spnichten Plattenstreifens oberhalb- ·der- BeUlgrenzell

Luftf'. Forsch., 1937.

"Behavior of a Plate Strip Und.er Shear and Com­pression. Beyond the Buckling Load"Translated into English:- N.A.C ..A., T.M. 870, 19.38.

124. Krupen, ph.. ~~d Levy, s."Large-Deflection Theory for End Compressi.on o£Long Rectangular Plates Rigidly Clamped AlongTwo- Edges H

N.A.C.A.. , T .. N. 884:> 1943 ..

125. Kuhn,_P. and. Peterson, J.P ...rrStrengthAna~ysi.s of Stiffened Beam.-WebsH

N ...A.. C.A .... :) T .M... 1364~ 1947.:-

If\)WI

126 ..Kuhn, p.~ peterson, J.P. and Levin,-L.R.fJA Summary of Diagonal Tension ff Part I and II.N.A,.C.A., T.N. 2661 and 2662, May 1952.

,127. Lahde, R. und wagner, R."Versuche zur Ermitt1ung des Spannungszustandesin Zugfe1dern"Luftf. Forsch., 'Nr. 13, 1936, S. 262.

See translation N.A.C.A., 'f.·,.M. 814, 1936:"Experimental Studies of the" Effective Width ofBu'ckled She'ets It

128. ""Leggel:t:., "1);-M.A."On the Elastic Stability of a Rectangular Platewilen'Subjec.ted to Variable Edge Thrust lt

Proceedings of the Cambridge Phil. Soc., Vol. 31,1935, P: 368.

129. Leggett, D.M.A."The Buckling of a Squar~ Panel Under Shear ~-Jhen

One Pair· of Opposite Edges isClamped lJ

R. & M. No. 1991, 1941. . .

130. Levin, L~R. and Sandlin, C.W., Jr."Strength Analysis. of Stiffened Thick Beam ~"ebslf

N'.-A.C.A. ,7~N. 1'820, 194.e,.

131. Levy, S. ,"Bending of Rectangular plates \vith LargeDefLections"N.A.C.A., T.N. 840, 1942.

132. Levy, S'.,"Square plate With Clamped Edges Under .NormalPressure producing Large Deflections" .N.A.C.A4, T ..N .. 847" 1942 ..

133-.. Levy, s.ffBuckling of Rectangular, Plates wi.th BUilt-InEdges." 'A.S .M.E.:t Trans. > VoL .. -64,. 1942, p ... A 171. ..

134. Levy, s. ."Large-Deflection Theory of Curved Sheet"­N.A.C.A., T.N. 895, 1943.

135.' Levy, S., Fienup, K.L., and Woolley, R.M.lTAnalysis of Square Shear Web Above Buckling Loadff

N.A.C.A., T.N. 962, 1945.

'136. Li, Y.;S."Theoretical and ExPerimental Study of ' the Behav­iour of Thin· Flanged Box Girders in Pure Bending lf

Thesis for degree of Ph.D. £n Univ. of'London, 1948.

l37~ Lungbottom, E. and Heyman, J.;.'~xperimental Verification of'the Strengths ofPlate Girders Designed in Accordance with theRevised British Standard IS3: Tests on Full S~eand on Model Plate Girders1f

The Institution of Civil Engineers, Great .. GeorgeStreet, tVestminster,cLondon s .. toJ.l, Struct. paperNo. 49, 1956, pp. 463-486.

138. Lundquist, E.-E.ifComparisoD, of Three Methods for. Calculating theCompressive Strength of Flat and Slightly CurvedSheets and Stiffener CombinationH

N A.C.A., T .N. 455.

139. Lundquist, E.E."Local .Instability of Symmetrical RectangularTubes Under Axial Compression"N A.C.A., T ..N. 686, Feb. L93S.

If\)

~I

140"

141.

142.

Lundquist 3 E .. E ..IfLocal Instability of Centrally Loaded Columnsof Channel-section and z-section tt

N~A .. C~A~, T .. N. 722, 1939.

Lundquist, E.E .. and Stowell, E.Z .."Critical Compressive Stress for Flat Rectangularplates Supported Along All Edges and ElasticallyRestrained Against Rotation Along the UnloadedEdges t1

N.A .. C.A .. , T~N. 733, 1942.

Lundquist, E.. E. and Stowell, E.Z."Critical Compressive Stress for OutstandingFlanges 11

N.. A .. C.A .. , T .. N.. 734, 1942.

147 .. Mackey,. S .. and Brotton, DeM ..HAn Investigation of the Behavior of a RivetedPlate Girder Under Load tf

Structural Engineer~ Vol. 30, No.4, 1952, p.73.

1480 Madsen, 10;ttReport on Crane Girder Tests"Iron and Steel Engineer, Vol .. 11, Nov~ 1941~

pp.47-97.

149. Mayers, . J. and Budiansky, B.tfAnalysis of Behavior of Simply Supported FlatPlat~s Compressed Beyond the Buckling Load intothe plastic Range"N A.. C.A., T.N. 3368, 1955.

143. Lundquist, E~E .. and Stowell, E.Z.tlRestraint Provided a Flat Rectangular plate bySturdy Stiffener Along the Edges of the Plate"N.A.C .. A., T.N. 735, 1942.

-144 .. Lundquist, E .. E., Stowell, E.Z., and Schuette, E.H.IIPrinciples of Moment Distribution Applied toStability of Structure~ Composed of Bars orplates U

N.A .. C.. A., W.. R. L-326, 1943.

145. Lurie, H..riLateral Vibrations as Related to StructuralStabilityHCa~if. Inst. TechnO', Guggenheim Aeron. Lab.,Rep~ No .. 2, 1950.

146 . Lyse, I.. and GodfreY:J H.."Investigation of Web Buckling in Steel Beams:!A.S.C.E .. , Trans., 1935, po 675.

150. Marguerre, K.TtDie {{ber die Ausbeulgrenz.e belastete platte ­Energieansatz und Differentia1g1eichungen1f

Z.A.M.M., Vol. 16, 1936, s. 353.

I1Plate Loaded Beyond the Buckling Load ­Potential Energy and Differential Equations"

151. Marguerre, K.flDie mittragende Breite der gedrllckten Platte"Luftf. Forsch., Vol. 14, 1937~ S. 121.

"The Apparent Width of the Plate in Compression lt

Translated into English: N.A .. C.A':l T.N. 833" 1937.

152. Marguerre, K.Hueber die Behandlung von St:abilitMtsproblemenmit Hil£e der energetischen Methode H

z.angew. Math. u~ Mech. 7 Vol 0 18) 1938, s~ 57.

nOn the solution of Stability Problems byEnergy Methods"

IJ\)\..rlI

153. Marguerre ~ K.TlZ.ur Theorie' der gekrUmmten Platte mit grosserFormHnderungU

Proe. 5th Int. Congr. for Applied Mech.~ Vol. 5,cambridge, Mass .. ~ 1939, - p. 93.

"On the Theory" of the CurYed, Plate. with LargeDisplacements fl·

158. "Massonnet, Ch."Le.- voilement des ,plaques planes'solliei.tees'

dans, leur plan" ~

A. I..P .C., Rap. f., 3e congres, Liege, Belgique,·septembre 1948, pp.• 291-30Q.

liThe Buckling of Plates"

154.. Marguerre, K. und ~effz, E.'~eber die TragfMhigkeit eines IHngsbelastetenPlattenstreif.ens nach ueberschreiten der Beullast fl

z. angew. Math. u. Mech.• ,Vol. 17, 1937> S. 85.

Tl.Qn . .the Load-ca:rrying-Gapac.i-ty -,of-----a- .Wagi.tudinallyLoaded plate Strip in the post Buckling Rangelt

155. Massonnet, Cn.riLes relations entre lesmodes normaux de vibrationet La stabilite de_s systemes elas"tiques"Bull. C.E.R.E.S., Liege, Tome I, Nos.1-2,. 1940.

'~he Relations Between the Normal Modes of Vibra­tion and the Stability of Elastic Systems H

159. -Massonnet , Ch."Recherches experimentales sur Ie "0ilement, del'ame des poutres a "be pleine ff

Bulletin duCentre d'Etudes, TomeS, 1951,pp. 67-240, au A.I.P.C., ~~bl.prel., "4e congrescambridge-Londres, .1952" pp. 539-555.

t1Experimental Investigations -of ·t'1eb Buckling ofPlate Gird~rsll

160. Massonnet, Ch."Recherches sur le dimensionnement et le raidissagerationnels de l'ame des poutres a ame pleine, entenant compte du danger ·-de voilement U

. Annales de l'Institute Technique du Batiment ~t

des Travaux Publics, NO- 71, nov. 1953,7 pp. 1062-1080.

If\)0'I

157; Massonnet, Ch.IIEssais de voilement sur·poutres a ame·raidie"tse' congres Int-ernational des Centres d r Informationde l'Acier. (~ee Ref.' 161)

"Buckling Tests of Stiffened Plate Girders"

-162. Massonnet , Ch."Stability Considerations in· the Design of SteelPlate Girders"A.S.C.E., Proc. -Vol. 86, No. ST1, paper .No. 2350,January 1960.

156. Massonnet, Ch."La stabilite dellame des poutres munies de.xa.i.disseur.s horizontaux .e.t so.Llic..i.tees-par. ,flexion.purerl

A.I.P.C., Mem., Vol. 6, Zurich, 1940-41, pp. 234-246.

liThe Web Stability of Longitudinally StiffenedPlate Girders Subjected to Pure Bendingtr

161.

I1Invest.igations·on the Design and the EfficientStiffening of l~ebs in Plate Girders, Taking inAccount Web Buckling"

Massonnet, Ch •.f1Essais de voilement sur poutres a ame raidierl

A.I.P.C., .Man., Vol. 14, Zurich, 1954) pp. 125~186)oU4cier~ ·NO· 2, ~eV:ier 1955, pp. 3-12.

HBuck~ing Tests of Stiffened plate Girders rl

163. Massonnet, Ch. et Greisch, R.flAlbaques permettant Ie choix rapide de 1 J epais,seur

de ll ame d i une poutre a moe p1eine et de11ecartement des raidisseurs vert~caux en tenantcompte du danger de voilement"A.I.P.C., Rap. f •. , 4e congre.s, Cambridge~ondres"1,952; pp. 299-308, ainsi que'Notes techniques publiees par 1a C.E.C.M.,Bruxelles, 1953, editeur Fabrimetal.

'.'Charts for a Plate Girder, E~,etermining the Web­thickness and the Spacing of Vertical StiffenerTaking into Account the' Factor of safety AgainstBuckling;' -

168., Milosavljevitch, M.IfSur 1a stabilite des plaques"rectangulairesrenforcees par des, raid~sseurs',et, s'ollicitees,it' 1a flexion et au,cisaillementU

A.I.,P_C.,- Mem~ ,Vol·.. 8,.l947,. pp,. 141-160.

Han the Stability of Rectangular plates Reinforcedby Stiffeners and Subjected to Bending and Shear"

169. Moheit" w."schubbeulung rechteckiger Platten mi.t' ei.nge-spannten RMndern fT ~

'Thesis Techn. Hochschule, Darmstadc y Leipz~g~ 1939,oder Stahlbau, '19.40, S. 39.

(~.~

lb4-~ _' Maulbe~t.sc~ ,J_.L...."Buckling of Compressed Rectangular plates withBuilt-In-Edges"A.. S.M .. E., APM, Vol. 4> 1937, p. A59"

165. Melan, E.HUeber die StabilitHt von St,;{ben> welche aus einemmit'Randwinkeln verstirkten Blech bestehenf1

3 .. Int. Kongress, ftlr'angew. Mechanik, Vol. 3,1930,s. 59.

flori, the Stability of Members Consisting, of a Web,and Edge Angles" .

166 . Meyerding"Knickung von lHngs- und querversteiften ebenen .Blechen"Techn. Berichte der Luftfahrtforschung, Bd. II,1944. '

f~he Buckling of Longitudinally and TransversallyStiffened Sheets"

1670 Miles, A.J."Stabi..lity of Rectangular plates ElasticallySupported at the Edges"Jour.Applied Mechanics, Vol. 3, 1936, p. A-47~

'I'Buckling of Rectangular Plates with.Clamped Edges'Due 'to'-Shear't

170.. Moisseiff, L.S. and Lienhard, F.tTTheory of Elastic Stability Applied to StructuraLDesign" .A..S.C.E., .Trans., Vo~. 106, 1941, p. ) ..052.

171. Moore, R.L."An Investigation' of the Effectiveness of'Stiffeners on Shear-Resistant, Plate Girder Webs T1

N.A.C.A.,- T.N. 862, 1942.

172. Moore, R.L~

.TlObservati'3ns on the Behavior of, AluminumA110yTest.Girders"A.S.C.E., Trans., Vol. No ... 112~ 1947, pp __ : 901-920.

173. MUller-Magyar:L _TlBeitrag, ZUID' Uberkritischen Verhalten eines dlinn~,

wandigen, verstei£ten Plattenstreifens unter Druck1,

Federhofer-Girkmann-Festschrift, Verlag Deuticke,Wien, 1950. '

I1Behavior ,of' a Thin Stiffened Platestrip underCompression in the ·post Buckling Region"

If\)-J

I

174. Nadai', A."ElaStische Plattenl~

spr~ger-verlag,."Berlin,. 1925.

"Theory of Elastic' Plates" (Book)

1,80. P£lHger,. A."StabilitHtsproblem.e der Elastostatik~'

Springer-Verlag,. Berlin,. G8ttingen,:. Hei.delberg,1950,.•

"Elastic Stabili.ty~f" (Book)-

183,. Reimtzhuber, F.UBeitrag zur Berechnung gedrUckter, dlInnwandigerProfile oberhalb der Beulgrenze"Luftf. Forsch., Vol. 19, 1942, S. 240.

175.

176.

Nagel, H."gtabilitHt gedrUckter Rechteckpl?tten mitstreifenweiser konstanter DickeTt

Diss. T.R. Hannover, 1942.

"The Stahi·lity of' a Compressed Rectangular Platewith Piecewise constant Thicknessll

N81ke, K.·'·£i-egangsbeahmg·-tier'·"1~eCh1:eC1q11Q.'tte':m1't--e1.nge-spamiten,LlingsrHnciern" '.Bauing •. , Vol. 17, 1936, S. 111, Und· .lng'. 'Archiv, yol. 8, 1937, s. 403.

"Buckling strength of Rectangular Plates withClamped Edges 11.

181.

182.

Pippard, A.J.S., Sparkes, S.R •. , and Chapman, J.C.'''Experiments on Flexure of Rectangular Box

Girders .on Thin Steel Plating"Colston papers, Symposium on Engineering..Struc­~es, Bristol, 1949.

pride, R.A. and Heimerl, .G.J ..llPlast'ic Buckling of Simply 'Supported Compressedl'lat'eS"uN.A:C~A., T.N. 1817, 1949.

If\)CDI

177. anat, E.T. and Drucker, D.C."Inelastic Instability ~d Incremental Theory ofplasticity II ,_ ,o--_r. __.,

J. Aero. Sci)~ Vol. 20'j 'No. 3, March 1953, p.181.

17,g .; .·.p..eters,,,'~.-G.;.

"Buckling Tests of. Flat. Rectangular Plates UnderCombined Shear and .Longitudinal 'Compress~onn

N.A.C.A.. , T .N.· 750, 1.948. .

179.- PflUger, A.flZum Beulprob1em.der anisotropen Rech-teckplatte"Ing. Archiv, Vol. 16,1947,.5.111/20.

"an th.e Buckling of the Anisotropi.c Rectangularpiatell

"Contribution to the-problem of Compressed, Thinp+ofiles Beyond Bucklingtf

184. Reissner" 'E.IlBucklingof· Plates with Intermediate RigidSupper,tst' "-J. Aero~. Sci. ,Vo.l.. 12, 1945:1 p. 375.

185. Reissner, H."Ueber die Kni.cksicherheit ebener Bleche"zentralblatt derBauverwa~tung, 19-09, s. 93.

"Qn the Buckling of Plane Plates"

• ~ 1 ...... ~

186. Rendulic, L~

HUeber die StabilitHt von StHben" welche auseinem mit-Randwinkeln verstHrkten Blech bestehen"Ing. Archiv, Vol. 3, 1932, s. 447.

"On the Stability of Members Consisting of a'WebPlate and Angles"

187. Ritz, w.ttueber eine neue Methode zut~ LHsung gewisserVariationsprobleme der mathematischen Physik"Journ. f.d. reine U'. angew. Math .. , Vol. 135"1909, s. 1.

nOn.a N~w Meth.od for Solving Certain Variationaliroblems'-' in the :Fie1.cl'6E~atnemati:ea:1''Phy'Si'C~-U

188. Rockey, K.C. .... "The Design of Intermediate' Vertical Stiffeners

on ~'1eb Plates Subjected to ShearnAluminum Development Assocn., Tech. Memo No~ 295C,(British) .

189. Rockey, K.C."Shear Buckling of a Heb Reinforced by VerticalStiffeners and a Gentral Horizontal Stiffener"I.A.B~S.E., Publ .. Vol. 17, 1957") p .. 161.

190~ Rockey, K.C. and Jenkins, F.:rThe Behav'ior of Web Plates of Plate GirdersSubjected·to Pure Bending"Structural Engineer, Vol. 35, No.5, 1957, .

..pp .. 176-189~

191. Rockey, K.C."t..Jeb Buckling and plate Girder Design"Engineering (36 Bedford St., London, W.C. 2),Vol. 185, No. ~800, p. 312, March 7, 1958.

192. Rockey" K~.C.

"web Buckling and the Design of Web Plates'"The Structural Engineer" February,. 1958Discussion on the paper:The Strtic tural Engineer, september, ~958 •.

193.· Rode, H.H~

ffBeitrag ZI..lr Theorie der KnickerscheinungenJT

Eisenbau, Vol. 7, 1916, s. 121,. 157, 210, 239und 295 ..

"Contribution to the Theory of (Plate) Buckling lt

For that time a very advanced paper written bya man with wide experience in designing plategirders.

194. RoS,· M. and Eichinger, A.On inelastic plate buckling.I.A.B.S.E., F. Rep." 1st Congress, Paris, 1932,p. 144.

195. Sattler, K."Beitrag zur Knicktheorie dllnner Plattenr!Forschungsanstalt Gutehoffnungshlltte,Mitt~, Vol. 3, 1934/35, S. 257.

"Contribution to the Buckling 'Theory of ThinPlates"

196•.Sazawa, K. arLd Watanabe, ~.

"Buckling of a Rectangular Plate with FourClamped Edges-·-Re-Examined with Improved Theory"Repts. Tokyo Imp.Univ .. Aeronaut. Research Inst.,Vol. 11, No. 143, 1936.

197. Schapitz, E~

'~eitrMge zur Theorie des unvollstRndingen Zugfeldes"Luftf. Forsch., Nr. l4~ 1937, S .. 129.

"Contributions to the Theory of. th,e Incom"pleteTension Field"

I£\)

'"t

203. Schleicher, F.-"Stab:i?-~:cH.tsprobleme-vo~lwandi.ger Stahltragwerke ..

Uebersicht und Ausblicklt

Bauing-., Vol. 15,. 1934, S. 205.

198. Schapitz, E."F_estigkeitslehre fUr Leichtbaun

Deutscher I~g. Verlag G.m.b.H.; DUsseldorf.

"Strength of Materials for Light Gages Steeland Aluminum Structures" (Book)

199. Scheer., J."Neue -Beulwerte ausgesteifter Rechteckplatten"Stahlbau, Vol. 22, 1953.

"New Buckling Values of Stiffened RectangularPlates ll

~2'9<3.. SClleer,~ ;;l•.HZum Problem der 'GesamtstahilitHt von einfach­symmetrischen I-TrHgernJI

Stahlbau, Vol. 28, 1959, S. 113, S .. 165 ..

"an the Problem of the Complete-Stability*of Simply Symmetric Girders with I-Sections"

* How does _web buckiingaffect lateral bucklingof the beam and vice versa? In a Doctor_f~;

dissertation the author investigates theinteraction of these two stability cases.

f.04.

. 205.•

"Stability ,Problems of Plate Structures .-, Surveyand butlook" .Contains.smal1. tabula of optimum st~ffneS5 forstiffeners ..

Schleicher, F .."Einfluss der Querdehnungauf di.e Stabilitlit vonStahlplatten fl

Stahlbau, Vol. 8, 1935, S. 7.

"The Influence of Poisson's Ratio on the Stabilityof Steel Plates"

Schleicher, F •"Einfluss der StabilitMt· der Stegbleche auf dieGestaltung vollw3Ildiger BalkenbrUckentt

I.V.B.H .. , Vorb., 2. Kongress, Berlin-MUnchen,1936" S. 1391.

IJThe Influence of the Web Stab.ility on'the Design,of Plate Girder .Bridges U

IWoI

201. Schleicher, F.. .'~-eK-ni-ckspa.nnUng:en-von ::ei:rrgespannten, 'recllt­eckigen Platten"Mitteilungen ·derForschungsanstalten Gutehoff-".nungshlltte, Konzern 1, Heft 8, 1931.

,".-.-

UBuckling Stresses of Rect~gular Plates withClamped·EdgesH -

202. SChleicher~ F.UStabilitHt leicht gekrl:lmmter RechteckplattenH

I.V.B-.H.,·Abh., Vol. 1, zHrich; 1932, S .. 433.

"The Stahil:ity o£-Sl:ightly Curved RectangularPlatesn

206 • Schleicher, F •. und Barbre, B.nStabilttHt·versteifterRechteckplatten mitanfHnglicher Ausbiegung"Bauing. Nr. 18, 1937, s. 665.

nOn the Stability of Stiffened Rectangular Plates~aving Initial Deflections"

207. Schleicher~ F."Unelastische Beulung versteifter Stegbleche'·Bauing .. ~ Vol. 20, 1939, S. 217.

nlnelasticBuc~lingof Stiffened I-lebs n

208. Schleicher, F.flU~ber die B2ulungvQn Re"chteckplatten mitanfHng1icher AusbiegungnForschungsh .. aus do Gebiete do Stahlbaues, Nr. 6,1943,. s. ,146.

nOn the Buckling of Rectangular Plates withInitial-Deflections"

209. Schleicher, F.1'Taschenbuch fllr Bauingenieure, Erster Band,tSpringer-Verlag, Berlin, G8ttingen, Heidelberg,1955.

"Handbook for Civil Engineers"

210. Schmi~den, C."nas Ausknicken versteifter Bleche unter

Schubbeanspruchungt t

z. F1ugtec~. u. Motorluftsch .. , Vol. 2:1, 1930,s. 61. .

"The Buckling of Stiffened Sheets in-Shear"Translated into English by U.S~ Experim.entalModel Basin,NC? .. 31, 1936.

211. Schnadel, G."Die ueberschreitung.derKnickgrenze bei

diinnen .platt-en"3. rnt. Kongress. fUr angewandte Mechanik,publ., Vol. 3;.Stockholm,1930, s. 73.

"Post. Buckling Behavior on Thin Sheets"

212.- Schuette, E.H. and McCulloch, J.C~

"Charts for the Minimum weight Design ofMultiweb Wings in Bending"N.A.C.A., T~N. 1323, 1947 ..

213. Sc~, T.E."Die quadratische Plat;te- bei Schubbelastimg.·oberhalb der BeuIgrenzen

rng. Arcbiv', Vo~. 1], 1949, S. IIi•.

liThe Square plate Under She~ Beyond BucklingJT

214. Schwerin, E.'"ueber die Knicksicherheit ebener Bleche beL.,exzentrischer Randbelastungr•

z. angew. Math. -u. Meeh. ,.-Vol. 3', ..1923, S. ~22 ..

"On Buckling of. Eccentrically Loaded> Plane Sheets"

'215. Scott,. M.. and. Weber, R..L."Requirements for 'Auxiliary stiffeners Attachedto Panels Under Combined Compression. and Shear: tr

N.A.C.A , T.N~ 921, 1943.

216. sechler', E.E.f~he Ultimate Strength of Thin Flat sheets in. Compression" .

Guggenheim Aeron. Lab., Calif. lnst. of. Teehn.,.Publ.· 27, 1933.

'217. Sechler, E.E."Stress 'Distributi.on in Stiffened panels· UnderCompressionfl

J .. Aero .. ~ci., Vol. 4, "1937, p. 320.

218. seide,p. and Stein~ M~

"Compressive Buckling of. Simply Supported placeswith Longitudinal Stiffeners"N.A.C.A., T.N .. 1825, L949.

219 • .Se'ide ,. P."The Effect.of .Longitudinal Stiffeners Locatedon One Side of a plate on the Compressive Buck1irigStresso£ the Plat~-StiffenerCombinations"N.A.C.A., T.N. 2873, 1953. "

.~~~-

I\....aJI--'I

220. Seydel, E. .HUeber das Ausbeu1en eines orthotropen Platten­streifens (einer sehr langen, rechteckigen,versteiften Platt"e) bei Schubbeanspruchung"Proc .. of 3d Int. Congr. for Applied Mechanics,Vol .. 3, Stockholm, 1930.

"On the Buckling of an orthotropic Plate (BeingExtremely Long, Stif-fened and of RectangularShape) Due to Shear"

221. seydel, E."Be{trag zur Frage des Ausbeulens versteifterPlatten unter Schubbeanspruchung"Jahrbuch, Deutscher Verein fUr Luftf. Forsch.,19~0.~ s. 235 ..

"Contribution on the problem of Buckling ofStiffened Plates Due to Shear"Translation into English: N A.C.A., T.M. 602, 1931.

222. seydel, E."Ausbeul-Schublast rechceckiger platten (Zahlen­beispiele und Versuchsergebnisse)" .z. Flugtechn. u. Motorluftsch., Vol. 24, 1933,s. 78~ .

"Buckling of Rectangular Plates Under Shear ..It~erical Examples and Test ResultsI'

223.,._~ydel, E."Das Ausbeulen von rechteckigen'ib orthogonalanisotropen platten bei_Schubbeanspruch~g"

Ing~ Archiv, Vol. 4, 1933, s. 169~

"On the Buckling of erthogonal AnisotropicPlates Under Shear"

224. Sezawa, K."Das- Ausknicken vonallseitig befestigten undgedrUckten Rechteckplatten"z .. angew ... Math. u ... Mech., Vol .. 12, 1932, S .. 227 ...

"The Buckling of Compressed Rectangular plates"

225.. Shibuya, I."A Method of Estimating the Theeiretical BucklingLoad from Experiments on Rectangular Plates"Proe .. 2nd Nat .. Congress for Applied Mechanics,Japan, 1952, p. 139.

226. Sievers, H. und Bornscheuer, E.- '"Ueber dis Beulstabilicllt durchlaufender Plattenmit drehsteifen LHngssteifen"Stahlb~u, Volo 22, 1953, s. 149.

liOn the Stability of Continuous Plates with Longi­tudinal Stiffeners Having Torsional Rigidity"

227. Skan, s.w. and Southwell, R.V .."On the Stabili.ty under Shearing Forces of- aFlat Elastic Strip"Froc .. Roy. Soc., Series A, Vol. 105, London,1924, p .. 582.,

228. Sommerfeld, A."Ueber die Knicksicherheit der Stege von Walz­werkprofilen"z. f. Math. _u. Phys., Vol .. 54, 1906., S .. 113.

"On the Buckling Safety of webs of Rolled Beams"

229. Sparkes, S ..R~tiThe Behaviour of the webs of Plate Girders"Welding Research, Dec. f947, p. 4.

ILvI\)I

230. Sparkes, S.R., Chapman, J .. C.. , and Pippard, A.J .. S."Experiments on the Flexure of Rectangular BoxGirders of Thin Steel Plating".Research, Eng. Struct. Suppt., 1949, p. 61.

231. Stein, M. and Fralich, R.W."Critical Shear· Stress of Infinitely Long, SimplySupported Plate with Transverse Stiffeners"N.A.C.A., T.N.' 1851, 1949~

232. Stein, M. and Neff, J.'TBuckling Stresses of Simply Supported -Rectangularplates in Shear"N.A.C.A., T.N. 1222, 1947.

233. Stein, O."Die StabilitHt ,der BlechtrHgerstehbleche imzweiachsigen SpannungszustandT'

Stahlbau, Nr. 7, 1934, S. 57.

"The Web Stability· of Plate-Girders Under aTwo-Dimensional State of Stress"

234. Stein, o.I1StabilitHt ebener Rechteckb-leche unter Biegungund Schub"Bauing. Vol. 17, 1936, S. 308.

t~The_St-ability<)f-Plane Rec'tangular ·Sheets UnderBending and Shear'"

235. Stiffel, R."Biegungsbeulung versteifter Rechteckplatten"Bauing-., Vol. 22, 1941, 5. 367.

"Buckling. of Stiffened Rectangular Plates UnderBending"Gives design chart for a longitudinally stiff­ened plate" with stiffener at a quarter of theplate depth.

236. StowelL, E..Z."Critical Shear Stres of an. Infini.tel.y Long- Flat Plate with. Equal Elasti.c RestraintsAgainst Rotation Along the. Parallel Edges tT

N.A.C.A., W.R. L-476, 1943.

237. Stowell, E.Z.TtA Unified Theory of Plastic Buckling of Columsand Plates"N-A.C.A., T.N. 155&,1948.

238. Stowell, E.Z."Critical Shear Stress of an Infinitely LongPlate in the Plastic Regi.onTl

N.A.C.A., T.N. 1681, 1948.

239. Stowell, -E.Z. and Lundquist, E.E-.nLocal Instability of Columns with Channel andRectangular Tube sections"N.A.C.A., -T.N. 743) 1939.

240. Stowell, E.Z., Heimerl, G.J., Libove, Ch .. and.Lundquist, E.E.

HBuckling Stresses for Flat plates and· Sections"A.S.C.E. Proc. Vol. 77, July 1951 (Separate.No. 77)

241. Stllssi, F."Berechnung der Beulspannungen gedrUckterRecht­eckplatten"I.V.B.H.I; Abh., Band 8, Verlag Leemann, ZUrich"1947, S. 237.

"The Calculation of Cr:iti.cal Stresses of CompressedRectangular Plates lf

24-2. St{lssi, F.I'Zur Bemessung von Leichtbauten aus Stahl r ,

I.V.B.H., 5. Kongress, Schlussbericht, Portugal,1957.

"Design of Light Steel Structures"

JWW

I

243~ Sttlssi., F' .. , -Dubas,.~ ch .. etoubas, P ... "Le voilement de 1-' ama__ de-s poutresflechies,

avecraid~sseurau c'inqui~e' superieur"A ... I .. p.C .. Mem.7 vol.• , Zurich, 195T..

"Web Buckling of' plate Girders with LongitudinalStiffeners in the Upper Fifth Poi.Q.t of the Web"

244. Stllssi, F", Duba:s, Ch. et Dubas, P ..TILe voilement del'ame 'des RPutres fl~chies,avec raidisseur au cinquieme superieur.Rtude complementaire"A.. I ..p .. C.Mem"" 8 vol .. , Zurich, 1958.

"Web Buckling of Plate-Girders with .Lo~gitudinal

Stiffeners in the upper Fifth Point of the Web ..Further SJ:udy'"

245. Stllssi, F·.. , Ko'llbrunner, C..F. und Walt, M.."Versuchsbericht {{ber das Ausbeulen der auf ein­seitigen, gleicbmHssig und ungleichmMssig ver­teilten Druck beanspruchten PlattenT

'

lnst. f. Baust. a.d. E.T.H .. , Mitt. Nr. 25,:Verlag Leemann, Zllrich, 1951.

TlTest Report on Buckling of Uniformly and Non­Uniformly Compressed"Plates"

u .'24"6. Stussi, F., Kollbrunner, C.. F.. und ~.;ranzenried., W*

, "Ausbeulen rechteckiger·platten unter Druck,Biegung und Druck mit Biegung"lnst.• f. Baust .. a.d .. E.T.H .. , Mitt. Nr. 26,verlag Leemann, zllrich, 1953 ..

"The Stability 0'£ Rectangular Plates Under Uniform·Compression, Pure Bending,. and'Compression andBending" . - .,ContaiI;l5 calculations which check and improvevarious k-values obtai.ned until 195'~" They areconsidered. to be the, most accurat'e bucklingvalues. In connection wi.th this numerical datais a folder containing a chart with k-values(see next reference).

247 • stUssi, F., Ko.llbrunner,. C.F·... und wanzem:i.ed, .R_llTabellen der Beu1.werte." k ff

rT ..K.V.S.B .. ,zllri.ch, ~ ·1953.

trTables of' Buctling jTalues k"

248. Taylor, G.I ..."The Buckling Load for a Rectangular Plate. wi.thFour Clamped Edges"Z .. angew .. Math .. u .. Mech., .. VoL.... 1.3, 1933, p.147 ..

249. ThUrlimann, B."Strength of Plate,Girders."A.I.S.C .. National Engineering Conference,.'proceedings 1958, American Inst:ltute. of SteelConstruction,.. New York.

250. Timoshenko, S. _"Einige StabilitM.csprobleme der E1astizi.tMtstheori.e"zeitschrift f& Mathematik und Physik, Vol. 58,1910, S. 337.

·"Some Problems of Elastic Stabi.li.ty1t

251. Timoshenko, s .."ueber -die S'tabilitlit versteifter Platten"Eis~nbau7 Vol. 12, 1921, s~. 147.

Hon the Stability of sciffenedPlate·sTJ

252. Timoshenko, s."Stabili.ty of the Webs-of plate Girders Tt

Engineering, Vol. 238, 1935, p. 207 ....

253. Tlmoshenko, S'."Theory of Elastic Stabi1.ityfl (Book)McGraw-Hill Book Company, .New York and London,1936.

IW+=­

I

254.. Torre, K."Vorschlag filr die praktische Beulberechnungversteifcer Rechteckplatten ll

Stah1bau, Heft 10/11, 1944 ..

"Suggestions-for the practical Calculation ofCritical Loads of Rectanguiar Plates lf

255... Trefftz, E ..HEin Gegenstllck zum Ritzschen verfahren"

2 ... Kongress fllr angew ... Mech ... , Abh., ZUrich,1927, S~ 131-137.. -

'fA Method Opposite to the Ritz Procedure"

256. Tref~tz, E... >

t1Zur Theorie der StabilitMt des elastischenGleichgewichtes ll

z. angew .. Math .. u. Mech ... , .'la.l. 13, 1933, 5 .. 160 ..

"On the Elastic Stability of Equilibrium Can­figurations 1t

257. Trefftz, E .. and Willers, F .. A."Die Bestimmung der Schubbeanspruchung beimAusbeulen rechteckiger Platten"z. angew .. Math. u. Mech~, Vol.16, 1936, s. 336.

"The Determination of the Shear Strength ofRectangular plates in the Moment of Buckling"

258. Wagner, H.. ."Ebe:D.e BlechwandtrHger mit sehr dilnnem StegblechT1

Z .. Flugtechn. u. Motorluftsch., Vol. 20, 1929,s. 200, 227, 256,279 u. 306.

"plate Girders with Extremely Slender webs fl

25 9 • i.J'ang , C .. T .."Nonlinear- Large-Deflection Boundary-Valueproblems of Rectangular Plates:'N.A.C.A., T.N. 1425, 1948.

260.· Wang, C.T. and zuckerberg, H.rtInvestigatiolJ, of. S'tress Distribution in Rectan­gular plates with Longitudinal Stiffeners UnderAxial Compression after Buckl.ingtl

N.A.C.A., T.N. 2671, ,1952.

261. Wang, T.K."Buckling of Transverse Sti.ffened plates Under ShearnJourn. of Appl. Mechanics, Vol. 14, No.4,Dec. 1947, p. A-269.

262. WHstlund, G. and Bergman, St."Buckling of Webs in,Deep,Stee1 I-Girders rt

Report of the Institution of Structural Engineeringand Briqge Building, Stockholm, 1947, p. 206 orr.A.B .. S.E-., Publ., Vol. 8" -1947 ,p. 291.

263. Way, S .."Stability of Rectangular plates Under Shear andBending Forces"Journ. of App1. Mechan'ics, Dec. 1935, andA.I.P.C., Rap. f., 1936, pp .. 631-638. '

264.. Weidlinger, P."Aluminum in Modern Architecture"Reynolds Metals Company, Louisville, Kentucky.,Vol. 2, 1956.

265. Windenburg, D.. F."The Elastic Stability of Tee Stiffeners H

U.S .. Experiinental Model Basin, Rep. 457" 1938.

266. Winter, G."performance of Thin Steel Compression Flanges!lr.A ... B.S.E. Pre1. Publ. 3rd Congress, Liege, 1948.

267. Winter, G."Post-Buckling Strength of Plates in Steel Design"I.A.B.S.E., F. Rep.,.l952, p. 268.

IW\.T\

I

2680 Young, J ..M. and Landau, R.E.- "A Rationa~ Approach to the Design of Deep

Plate Girders"Instn; Civ. Engrs., Prac., Pt. 1, Vol. 4,1955, p. 299. -

274. Tall-, L. and Ketter,- R.L."On -the Yi.eld Properties of Structural. SteelShapes"Fritz Engineering Laborat:ory Report No. 220A..33,Lehigh University, 1-958 ..

ADDITIONAL REFERENCES

* *- * 275. Thllrlimann, B. and Eney, W.J.'Modern Installation for Testing of LargeAssemblies Under Stati.c and Fatigue Loading"'Society for Experimental Stress Analysis,proceedings, Vol. XVI,- No.2.

269. Conyers; A_L. and Ozell, A.M.~...RepDrJ:~ . Tr.ansf.er- .of -Stre&SeS--in---Wel4edCover Plates tl

-

To be published in the Welding Journal, 1960.

270. Dill, F.H."A Report on Transfer of Stresses in Welded

Cover Plates"Appendix. - Application to Design.To be published in the Welding Jourhal, 1960.

2 71 ~ Haaijer, G. and Th{fr1imann> B."On Inelastic Buckling_in Steel"Proceedings of the ASCE, Paper No. 1581, April­1958.

272. Kusuda> T. and ThHrlimann, B.-"Strength of Wide Flange Beams Under Combined

Influence of Moment, Shear, and Axial Forcet.fFritz Laboratory Report No. 248-1, LehighUniversity, May 1958.

273.' Mueller, J.A."Stresses in Cover Plates and Bearing Stiffener-sri

To be published in ~he Welding Journal, ~960.

276. Timoshenko, S. and MacCUllough, G. H.TtElements of Strength of Mate.rialsH (Book)D. van Nostrand Com.p~Y_3 Inc-., New York andToronto, 1954. -

JW0'I

Graphical Summary of ReferencesCountry

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1930 1940 1950 Year

Part 1:

-1-

THE TEST GIRDERS

1.1 Introduction

The purpose of part 1 is to describe the test girders

and the physical properties of materials used. Then, based

on this information, standard reference values such as

"yield loads", "plastic loads", "critical loads", and com-

puted deflections will be established. The organization

of the test ,program must first be, described.

A girder section can be subjected to bending, shear, or

a combination of· both these loadings. In this research pro­

ject all three conditions were investigated. Consequently,

three different test setups were used as shown in Figs. 1.1,

1.2, and 1.3. This cla.ssifies the thirteen..plate girders

into the following three groups:

Grou.p shown in subjected Girders,.

to

1 Fig. 1.1 bending GI, G2, G3, G4, G5

2 Fig. 1.2 shear G6, G7

3 Fig. 1.3 combined El, E2, E4, E5, G8, G9

Throughout the entire project the girders are termed as given

in the last column of this table.

--2-

The cross' section of some girders changed wi·thin their

lengths _. ,~he.,reason for th~s design was· to confine failure" .

t9: ac.ertain'reg1on whose loading eondi tiona were well

defined. Thi's region was the test .section proper as indi­

ca'ted ·in Figs.l~l an<l1.2. The el:1d sections, flanking the test

see~'ion, onl-y diff'ered in web :thickness for the 'first· group,

.whereas in', t~e second group cover plates .. were also added. over

a. ,por'ti'on 'of their length. In the third grou.p the cross

se~tion did cnot change and the entire girder was the test

section proper. The rour girde~s termed El, E2, E4, and E5

w~re fabricated by splicing the undamaged end sections of

~.he ·corresp'ondingly numbere'd girders Gl, G2, G4 and G5.'· an'd

.reinforcing .them with cover plates-.

Each girder was subjected to at least two ultimate load

tests. After caus~ng failure in a particular panel) the

'load was remo~ed'and the panel reinfo~eed. All bending

girder' fail.urea, occurred in the compressio,n flange and thus

reinforcement consisted of welding small steel plates to

this flange. Diagonal ~nd transverse stiffeners were used

to s,trengthen the girders of the other two groups. Since

no major deformati6ns were caused in panels adjacent to the

one which failed in th~ first test, referr.ed to as. Tl, a

second test, T2, could be conducted. In some cases this

process waf3 repea.ted and additional tests', such as' T3 and

T4, were carried out.

-3'"

'Of all the po~sibl~·parametGr~ influencing the ca~rying

capaoity of,plate girde~s, the investigatio~ was reBtric~ed

to the ,.following four:

'1. Loa.ding ootidi t1on: ~ ::; '7:/0 -shear stressnormal stress

'2,. Type of cross section': various shapes of eompr. flanges

3. Web s'lenderness: ~ = bit = web depthweb thickness

4. stiffener s,pacing: a == alp = panel lengthweb depth

The first parameter was, taken care,of by choosing the three

t'est setu,ps ,pr,eviously mentioned. The. second ,parameter' was

of special import,ance to the bending girders, wherefore

three, ,different shapes of the co~pressi~n f~angeswere

chosen as illustrated with cross sections t, II, and III

shown in Fig. 1.4. Denoting with na,n the stiffener spacing,

"b" the web d.epth, and nt" the web thickness, the third and

fourth parameters completely defined the, shape of a web

panel. In the test 'program, the third parameter was varied

by b~ilding pairs of girders which only differed in the web

slenderness, such as G2 and G4, or G3 and G5. Finally, the

fourth parameter was accounted for by subdividing the test

section into panels with different lengths. After failure

occurred in a longer panel, it was reinforced and thus

failure could be, forced to occur in a shorter panel.

-4-

The parametric values of all the girders 1 test sections

are listed in Table 1.1. The added sketches indicate where

each girder failed, how the obtained tests were designated,

and where reinforcement plates were welded to the flanges

or webs. Taking as an example girder E4, the sketches give

the following information: The first test of this girder,

Tl, caused failure in the left-hand end panel whose stiff-\

ener spacing was 1.5 times the web depth. The girder was

then reinforced by subdividing each of the two larger

panels with new transverse stiffeners. Thus failure was

roread ,to occur in the right-half of the girder where the

spacing of the stiffeners was 0.75 of the depth4 This

happened in the panel adjacent to the loading stiffener

and furnished the second test, T2. Welding a reinforcing

stiffener across this damaged panel allowed for a third

test T3 in a panel whose aspect ratio was a = 0.,.

In the following sections the evaluation of girder

plate dimepsions is given first, followed by the determi­

nation of steel properties, and finally, the detailed

computation of specific reference values.

1.2 Girder Dimensions

-5-

After the general survey of the girders given in

Sec. 1.1, it is the purpose of this section to establish

the accurate dimensions of each girder. The overall

dimensions, as ordered, are given in Figs. 1.1, 1.2, and

1.3; for all practical purposes they can also be considered

to be the actual ones. However, this situation can not be

expected to apply to the size of the component plates and

measurements must be taken to determine their true dimen­

sions.

In illustrating the procedure used to obtain the dimen­

sions and the differences between ordered and actual dimen­

sions, the test section of girder Gl is used. The top

flange, web, and bottom flange of this girder are shown in

Fig. 1.5. Here, it is seen that at the ends of each plate,

a piece was cut off and used for coupons. These end pieces

were also used to obtain the width and thickness of the

corresponding plates. The dots in these portions are points

at which thicknesses were measured and the results are

recorded beside them. The averages of all the measurements

recorded were considered to be the true dimensions. Meas­

ured at 20 different locations, the web presented an

interesting finding. As readings were taken from the upper

edge to the lower, the thickness was found to increase, exceeding

the ordered quarter inch thickness anywhere from 1 to 10%_

-6-

This variation is due to the fact that the web was originally

cut from a plate whose width was 100 inches and the lower

edge of the web was located at the midspan of the rolls

during the rolling o,peration. The slight flexibility of the

rolls gave this increase of two hundredths of an in,ch.

Using the same procedure and layout of observation

points, the other girders' dimensions were determined and

are presented in Table 1.2. All subsequent computations

are based on these values and other data given in Figs. 1.1,

1.2 and 1.3.

-7-

1.3 steel Properties

A great amount of time and effort was spent in evalu­

ating the properties of the girders t component steel plates.

Because the property of paramount importance to this

research program was the yield str~ss, the major part of

this section is devoted to its definition and determination.

It will be seen that, although mild steel was specified for

all girder components and care was taken to obtain a uniform

yield level, a con~iderable scatter of results is unavoid­

able.

Tests on tension coupons made from the material under

consideration were conducted to determine the yield level.

At least one coupon was cut from each flange plate, unless

two or more flanges came from the same slab. In this case,

a single coupon was considered sufficient for the entire

slab. This s~me principle applied to the web plates and,

in addition, a limited number of coupons were cut trans­

versely to the platets longitudinal direction. The relative

location of both flange and web coupons in their respective

plates is shown in Fig. 1.5.

In Table 1.3 all coupons tested for the plates com­

prising girders Gl through G7 are listed.. The additional

coupons, needed to complete the yield stress evaluation in

the group of girders under combined bendin.g and shear, are

recorded in Table 1.4. The first columns of these tables

-8-

describe the location of the plates from which the corre-

sponding coupons were cut. Although the exact dimensions

of these plates already appear in Table 1.2, for the

~onvenience, the nominal plate thicknesses are tabulated

again. Each coupon is assigned a number as shown in the

third column. Besides its number, a coupon. is designated

further by listing its steel quality according to ASTM

specifications and its heat and slab numbers provided by

the steel manufacturer. It may be observed that, if two

or more coupons have the same slab number, they originate

from one and the same rolled piece. A common heat number

indicates that the steel of these coupons were taken from

the same furnace charge, therefore they must have the same

chemical composition.

Further listed in Tables 1.3 and 1.4 is the chemical

analysis procured from the mill, showing the carbon,

ma~ganese, phosphorus, and sulfur content of the steel.

In the following columns of the, tables are the yield stresses,

ultima4e stresses and elongations, all determined by the

mill according to standard practice. Finally, in the last

five columns are tabulated the results of the coupon tests

conducted at Fritz Engineering Laboratory~ The three

characteristic values of yield stress, ultimate stress and

elongation are listed here, together with the area reduction

at the fractured section and the rupture stress cr occuringr

over the reduced area. To -compare the laboratory results

~ ......'. ~

-9-

with those obtained by the mill, the former results need

further explanation.

Each coupon was machined to the dimensions given in

Fig. 1.6. These coupons conform with ASTM requirements

for plates over three-sixteenths of an inch in thickness.

(For plates below this value, specifications call for a

smaller coupon with a two inch gage length rather than the

eight inch length used.) Figure 1.6 is a typical data

sheet illustrating in detail the evaluation of pertinent

data of the coupon. Figure 1.7 is the corresponding load-

strain curve for this coupon. An extensometer was used to

obtain the strain for this figure and an electronic

recorder automatically plotted the resulting curve. The

abscissa is the average strain in inches per inch gage .

length, while the ordinate is the tension force applied to

the coupon. By converting load to stress, this d.iagram

could be considered as a stress-strain curve extending to

about thirty times the yield strain, only about one-eighth

of the complete diagram up to· the rupture point. Charac­

teristic of this diagram would be the straight-lined

elastic part, the yield level and the inception of strain

hardening. Also included in this graph are: the upper

yield point; immediately ~ollowing the lower yield point;

the dynamic yield level about which the load fluctuates

during yielding; and, finally, the static yield level which

shall be discussed further.

-10-

The static yield" level is the yield stress obtained

under a zero strain rate. This strain rate could easily

,be imposed by the 120,000 pound Tinius Olsen machine used;

a screw-powered type machine which allowed complete control

of the speed of the movable crosshead. When pronounced

yielding was apparent, the movement of this crosshead was

stopped after which the load settled to the static yield

level, Fig. 1.7. After about five minutes, the speed of the

crosshead was <again set at its former value of 0.10 inches

per minute. As seen, the resulting dynamic yield level

coincided with its previous value. This procedure was

repea~ed a second time in the yield zone where another

typical V-notch in the recorded load-strain curve occUrred.

It is generally known that the yield stress level does

depend o~ the speed used to test a coupon and increases

with higher testing speeds. However, the signifioant

research work carried out in Fritz Engineering Laboratory,

Ref. 274, correlates the dynamic yield levels obtained at

various strain rates and points out that this static yield

level is a material constant which. can be obtained more

accurately than the fluctuating dynamic yield level. Since

it is impossible to maintain any constant strain rate on a

steel element such as a plate girder, it is obvious that

the static yield level must be adopted as the significant

level in the testing of structural members. Only with zero

strain rate can complete correlation between both structure

-11-

and coupon be attained. Therefore, the yield stresses cry

hencefor~h mentioned in these reports will always be the

static yield stresses. As a consequence, the ultimate load

must be defined as the highest load which the structure can

statically maintain.

The results of these carefully conducted coupon tests

can certainly be used as added data to be collated for

statistical purposes. Of the many conclusions which may be

drawn from the two summary tables, o~ly the following are

mentioned. From Table 1.3 the seven t'hres-quarter inch

coupons show the scatter of yield level which mu~t be ex-

pected when plates of equal dimensions are rolled, even

though they origin.ated from the SaPI8 ingot. The one-half

inch,an~ ~hree-eighth inch web material also came from a

common ingot but differed in thickness and, thus, in the

extent o~ rolling. This resulted in a marked difference

in the static yield levels. Furthermore, the 'static yield

levels of the three-quarter inch plates were about 10%

lower than the yield stresses determined by the mill.

However, this percentage chang~s considera~ly with the

plate thickness and the chemical composition. For plate

thicknesses greater than three-quarter of an inch, this

reduction may well be as much as 25%, as seen from Table

Contrary to the aforementioned, it was found that for

the coupons cut from the one-eighth inch plates, CF 23 and

-12-

CP 47, the relation was reversed. Static yield levels as

much as 15% higher than the dynamic ones furnished by the

mill were observed. This was then believed to be a mistake

and additional coupons adjacent to the previous ones were

cut from the plate specimen and tested by both the fabri­

cator and the investigator. It can be seen from Table 1.3

that the results of these duplicate coupons, termed OF 23B

and OP 47B,were just about the same as previously obtained.

As stated before, the gage length of the mill and laboratory

coupons w~re two and eight inches respectively; the mill

coupons conformed to ASTM standards. It is interesting to

speculate as to whether the size causes such effects.

In summary, it must be emphasized again that the impor­

tant material property called "yield stress", as determined

by standard practice in the mills, is not adequate for

strength predictions in research work where structures are

subjected to static loads.

For the tubular compression flanges of girders G3 and

G5, a co~pression test was conducted on a short section of

the pipe rather than tension coupon test. Reference should

be made to Fig. 1.8 where the size of this stub column, th~,to.

load-deformation record, and the computed stress-stra.in

diagram are all shown. Also the wide scattering of wall

thickness in the tested pipe can be seen. The yield stress

was evaluated from the evident yield level.

-13-

Finally, the yield stresses of all co~ponent plates

are summarized in Table 1.5, grouped according to the

respective girders. The computation of all girder reference

values is based on the data tabulated here.

-14-

1.,4 Cross Sectional Constants

In this section will be presented the moments of

inertia for all girders with their corresponding section

moduli. To compute these values, it is necessa~y to

know the cross sectional shapes and dimensions. The former

can be found in Fig. 1.4, while the latter are summarized"'1-10

in Table 1.2.

A typical computation of the cross sectional constants

is carried out below. The procedure was first to find the

moment or inertia '1 about the Z-axis which was located at. z

the mid-depth of the web. Then, after determining the

actual centroid of the section, the moment of inertia about

the neutral ax~s was found by means of the parallel axis

theorem. Finally, dividing this value by the drstance to

the extreme fibers sa and eb , the s~ction moduli Sa and Sb

were 'obta.ined. The indices "a." and "b" distinguish between

quantities above and below the neutral axis respectively.

". ..

·-15-

Computation of Section Moduli of Gl·-Tl t Test Section

12.2.' )t' 0,160

AY = Qz/A = -15.0/31.59, ~ -O~47 in

!m = I z-(Ay)2A = 14,390 - 0·472x31.59

Sa = 25 + 0.47 + 0.43 25.90 in

eb = 25 0.47 + 0.76 =25.29 in

Sa = Inlea = 14,380/25.90

Sb = In/eb = 14,380/25.29

= 555 in:;'

== 568' in),

Following the above procedure, all.necessary cross

'sectiona'l constants were COnl.puted for the girders and are·

pre,sented in Tab'le 1.6. In the. first th~ee columns of this

'table ar~ 'givan the properties of the test '~ection, namely,

the moment of inertia 'lm and the corresponding section

moduli S~ and Sb. Next, the moments.of inertia of the

bending and shear girders' end sections~ Ie, a~e added.

Finally, some special moments of inertia are given in the

last column which will now be explained for each girder:

....16-

Gl. After the first test on this girder was completed,

its top flange width was reduced by flame cutting to

13.56 inches. Thus, for computations involving GI-T2

(second test of girder Gl) this new width must be used,

resulting in I = 12,210 in4 and a neutral axis at

y = -3.158 in.

G2, G3, G4, G.5. After completion of the first tes'ts of

these bending girders, a steel plate was welded on each

side of the top flange. Each of these two plates had an

area of one square inch, had the same distance from the

neutral axis as the centroid of the unreinforced flange,

and extended over the longest panel of 75 inches. Where­

from this new I-value is computed.

G6, G7. These values are the moments of inertia of the

sections under the reactions where cover plates were

a.dded, that is, re D shown in Fig. 1.2.

El. The outside cover plates of girder El were termi­

nated 75 inches from its ends and, therefore, two moments

of inertia are needed to compute deflections. The value

shown in the last column applies to the end portions of

the girder. Since the third test produced failure within

this region, the values without cover plates must be used

for calculations concerning EI-T3.

-17-

1.5 Reference Moments and Loads

This section is devoted to the computat ion of ,the fla.nge

moment, yield moment, and plastic moment with the correspon­

ding loads of the latter two. These moments are defined in

Ref. 7, p. 34. Their de~initions are repeated below with

the modifications needed to take into account the different

yield stresses of ~he component plates.

The flange moment, Mf

, is defined as the moment carried

by the flanges alone when the stresses over the flanges are

equal to the yield st~ess. For a symmetrical girder whose

yield stresses are the same for both flanges, this would

simply be computed as Mf =Afcryfh, where Af and cryf are the

area and yield stress of one flange and h is th~. distance

between the centroids of the rlanges. The actual girders

tested exhibited a certain degree of dissymmetry in shape

and yield stress. Therefore, the area and yield stress or

the compression flange are selected to be used for the com­

putation. Incidentally, the alternate use of the tension

flange properties would not lead to any great differences.

Computations show that their use could only give a value

lower by 2.5%. When more than one plate comprises a ~lange,

a weighted yield stress of the compression rlange was used.

This weighted stress, d , will be defined as (J =J:.Acr /r.!y y y

where A and cry are the areas and yield stresses of the com-

ponent plates and L indicates the-ir summat ion.

-18-

The yield moment, M , is the moment which initiatesy

nominal yielding in the most extreme fiber. In the case

where' the yield stresses of the flanges would be the same,

it would be computed as MY = crys, where the smaller value

of the section modulus, S, would be used. Since the yield

stresses of the flanges differed, the definition that

MY= cryasa is adopted, where crya and Sa are the yield stress

and section modulus of the compression flange. As in the

case of the flange moment, the value of the yield moment,

when computed using bottom flange properties, could be lower

than the defined value by only 2.5%. In accordance with the

procedure adopted previously, a weighted yield stress was

used when the flange.was composed of a number of plates.

The plastic moment, MP' is the limiting value of the

moment which would be reached upon applying an infinite

curvature to a section, neglecting the effect o~ strain­

hardening. Usually it is calculated as the product of the

girder 1 s yield stress and plastic modulus, Z. This method

assumes a section whose yield stress is constant for all its

elements. As such, it can not be used in computations in-

volving th~ test girders since most of their component parts

yielded at different stress levels. This moment will be

evaluated from the relation that MP = r..AcryyP' where the A

and cry are the area and yield stress of a section's elements

and yp is the distance from the plastic neutral axis, NAp,

to the centroid of each element.

-19-

COMPUTATION OF· PLA'STICMOMENT OFE2. ,

NA' ,.r F, '50 x 0.507

"'4.9 KsJ

Ya = 24.8 in .

,.[~Acry] a - [LAcry] b = 0

,474 + 362 + 17.69Y~ - (885 +17.69Ya} -355 -474 = 0 '

16.00 J( 1.00729.4k~i, ",

12,'(9. x 0,'769.,3S·6'ksi

l2 .19 x Oa77437~G ksi .

. IG~OO ~ 1,00729. 4.-.kS i .

Mp =2:: (Acry)yp

= 474 x26~07 +' 362 x 2$.19 + ~39 x 12.4 +

446 x' 12.6 + 355 x 25059 + 474 x 26.4~

M~ = 54,lOO'~-ih

This plastic neutral axis is found f~om the equilibrium con­

dition that ~he ,sum 'of the normal .forces over the entire

cross section mUB.t vanish. USing the subsc,~i.pts a and b

mentioned before , ,t,hi~ condition is "ex:pressed as

[tAcrYJ a . - !l=AcryJ b= o. As a sample computation, the plastic

moment of E2 has been calculated apove. All necessary'

static' yield stresses are listed in Table 1.5.

To calculate the yield and plas~ic loads, ,the spans Of

the girder~ enter.. Again, due to' t:pe' different· test setu,ps,

three groups are distinguished: 'bendi~g, shear, and combined

loading.

-20-

The bending group has a constant moment over the test

section, M = 150P. Thus the yield and plastic loads are

simply computed' as Py = My/150 and Pp = Mp/150, ,where the

moments are expressed in kip-inches and the loads in kips.

The shear group, although subjected to a relatively

small variable moment, was considered to be under pure

shear. Therefore, the yield load is the load that initiates

nominal yielding at the neutral axis in the web and is com­

puted from Vy = 't'yw1t/Q where Vy is the shear force at first

nominal yielding, ~yw the shear 'yield stress of the web, Q

and I are the static moment and moment, of inertia about the

neutral axis, and t is the thickness of the web. From

Fig.L2 it can be seen that V = P. Substituting this value

in the preceding equation and using the Mises yield con-

dltioh that cryw = 13' 'T:yw, the yield load will be evaluatedcr It

as p = yw where cryw is the yield stress of the web. TheY ITQ

plastic load is defined as the load which causes the web to

yield completely due to shear,- Pp :: aywAw/n, Aw being the

area of the web, Aw = bt.

The combined grou,p was subjected to both shear and

moment. Since the moment varied throughout the girderts

length, e' cross section in the failed panel was selected

at which the reference loads for each. test were to be

evaluated. This section was chosen to be at a distance of

one-half the web depth a~ay from·the maximum moment in the

panel or at the middle of ,the panel when its l'ength is less

-21-

than its depth. It is realized that this method of evalu­

ating the yield and plastic loads differs from the usual

procedures used for a beam. Thus, the "yield load is defined

as the load which initiates yielding in the critical cross

section of a girder. In general, yielding first occurs at

the intersection of the web and flange where th~ yield con-

dition, o =/0 2 + 3 2/ is used to evaluate the yield load.yw 't' ,

Substituting the values of (j =MY = 12..s2 and 't'_ VQ _ PQ-- .....

I 2 I It 2Itinto the equation above, where M = Px/2 and V = P/2 from

Fig. 1.3, the yield load for the girders under combined

loading will be

= crywJ(2,5x/2I)2 + 3(Qj2It)Z'

x being the distance from the end of the girder span to the

critical cross section. If yielding does not begin at the

aforementioned point, the bending or shear case discussed

before applies.

The plastic load of any single test on a girder is

de~ined as the load producing plastification at the critical

cross section of the failed panel,. The presence of shear

in the combined bending and shear group of girders reduced

their full plastic moments MP. For these girders, an ex­

pression for a modified plastic moment MPs was developed

from the following considerations. The stress condition

sketched on next page is the basis for evaluat ing MPs' (Ref'. 272).

It will be assumed that the flanges have fully yielded,

...........

--22-

I

----r--+------t-.~ -I-T " "~o'-i

~f-i

th,ere,by 'pI'o~1d,:tng the .'flange moment" Nr,' and' that a con-

stant normal stress' (j is present ,.,over the web accotrl:panied,

by the eonst~nt ~hearlng.,stres~~. From the sketoh, the

modified moment is : Mps. = Mi' + a~b ~.~. An expression

for ais obtained from the yield criterion ayw = la 2 + 3~2~

V Mpawhere 't = b,t =btx.. Substi tut1ng the value of C1 in tl;le,

.first equation gives Mps ;:: Mf + ~ tb 2 :Ja.;w- 3 (Mps/btX)2' •

After solving for Mps and.observing that Mps = Ppx/2,

2 -L j' 2 27JPp = xa Mf + aMw -(a-l)Mr

where .. the constant a = 1 + -ft(~) 2, and Mw is the portion

o·f the full plastic' momen,t M,p cont~ibuted by the web,

Mw = aywtb 2 /4. When a negative number results under the

radl~al sign, the shear case e~plained before must be used

to obtain Pp ,. Physic~lly this result'implies that the web

yi~lds due to shea!' befo:re 'the yielQ. stress is .reached in

the ~langes.

In Table 1.7 ar·e sUITJInarized the reference moments and

lo~ds for all test girder~. Unlike the bending and shear

gr6ups, which ha.d constant moments and shear's over their,.

test section's, the combined grou:p had a var'lable moment

over 1 ts test sections whlc"h re·sults in two or more yield

and plas,tic loads for' each girder.

-23-

1.6 Web Buckling Stresses

An additional reference value with which the obtained

ultimate load can be compared is the conventionally computed

web buckling stress or load. It is the objective of this

section to establish these stresses and loads for all the

girders ~

The general equation for the ideal critical stress of an"f

isolated web panel is

= krr2 E I----..-

12(1-,,2) /32

where 0cri and ~cri are the ideal critical normal and shearing1I2 Estresses, respectively. The ractor is a qonstant

12 (1- \12 )

dependent only on the material properties,'.that is, the

modulus of elasticity E and Poisson's ratio v, while ~ = bit

is the slenderness ratio of the web. Finally, the buckling

coefricient k is a variable depending on the loading and

boundary conditions and, in general, also on the panel's

aspect ratio a = alb. Values for this coefficient can be

:found in such literature as Ref. 73, ..,116, and 247.

Some detail information must be specified in order that

the web buckling stresses of the actual girders can be com~

puted. In general, the procedures of Ref. 21 and 52 have

been adopted for the details which follow:

-24-

1I 2 EThe constant, l2(1-v2 )' for steel plates is equal to

26,750 ksi.

Web panels are considered pin ended on all sides.

The proportional limit 'of the web material is taken as

a.8oy • If the ideal critical stress 0cri is less thanI

this value, it'is equal to the critical stress ocr,

0cri = ocr" Whenever it exceeds this value, the critical

stress ocr is found from a reduction procedure,

ocr = Gy(l - a.16~y), a relation derived from Eq. (64),cr or 1.

'Ref. 21. Similar ly 't cr = 't' (1 - a •16't"y) , where 't is they ~cri

shear stress.

When a moment gradient exists in a panel, the critical

section is considered to be at a distance of one-half the

web depth from the maximum moment in the panel. In the

case where the panel l s length is smaller than its depth,

this section is at the middle of the panel.,

The critical shear force of a panel subjected to pure

shear is computed as the product of the critical shear

stress and the area o~ the web, Vcr = ~crAw.

In all cases, the unsupported web depth "b 1t is taken as

the clear web depth, which is 50 inches for all girders.

Finally, when the neutral axis is 1/2 inch or less away

from the web's geometric center, it is assumed to

coincide with the centerline,

The general cases of bending, shear, and combined

loading are presented next,

-25-

F~r.bendl:pg, the general formula for the normal criti­

cal stress Ocr! applies. The k-value is the only remaining

unknown. Since all the girders except GI-T2 had their

neutral axes less than 1/2 inch away from the web's geometrio

center, the k-value is k = 23.9. In GI-T2 the neutral axis

shifted 3.62 inches down from the web's centerline and thus

the co~pressive stresses a~e higher than the tensile stresses.

In accordance with Ref.52, this leads to a k-value of

k =18.6. The critical load Per is determined from the re~

lation tha.t o·cr = MerY/I, where Mcr = Pcrx/2, see Fig. 1.1.

For.shear, the general formula for the critical shear-

ing stress ~crl.app11e8. The buckling coefficient of

k = 4.00 +~ is used when the panel's aspect ratio aa

is equal to or less than unity, and k = 5.34 + 4.go is used. a

when a. ;:"1. In .this ease, Per 1s evaluated from 1;cr = Vcr/bt,

where Vcr = Per, see Fig. 1.2.

For combined bending and shear,

where overi is the equivalent ideal critical stress for com­

bined loading according to Ref. 52, cr the extreme bending

stre'ss of the web, (j ::: MY/I, and 't the a,verage shearing stress

~ =·V/bt. M and V are the applied moment and sh~ar respec­

tively :Ln the..conside:red qross ,s·eetion o The formula above is

only applicable to girders whose neutral axes coincide with

their web's 'geometric centers and as such ap.plies to a.ll the

-26-

girders of the combined group whose axes were all less than

1/2" away from the centerline of the web. After reducing

the ideal stress for inelastic action, if necessary, .t~e

cr it ieal loadPer is obtained from the equation 0vcr=!o2+3't'2',

where cr and't' are both functions of 'P, the applied load.

As an example, the critical load of the first test of

E2, a girder under combined loading, shall be computed.

From the tables and figures of previous sections the proper-'

ties of E2-Tl are as follows: a = 3.0, ~ = 99, Aw = 25.3

I = 39,620 in4 and 0yw d 34.9 ksL From Table 1.1 it is seen

that the long panel failed iti this first test. Since a

the critical stresses due to moment and shear are evaluated

moment gradient exists in this panel, the critical cross

= 37.5 ksiJ(O.0394P)2+ 3(O.0198P)2! = O.0522P

,(0.0 394p 2+ (9 •0198p\ 2 0 •00 139 P65.2 \ 15.8 7

°vcri =

The proportional limit ,is 0.80y = 0.8x34.9 = 27.9 ksi.

section is at a distance of 25" to the left of the center

bearing stiffener or x = 125" from the end of the girder.

Knowing this data and using ka = 23.9 and k~ = 5.79 (a>l),

as 0cri = 65.2 ksi and ~cri = 15.8 ksi. The stress at the

compressive edge of the web is a = MY = P.125 25 = O.0394pI 2.39,620

~s~ , and the average shearing stress over the section is

't' = :!- = P = 0.0198P [}rs~. Substituting these valuesAw 2.25.3

into the equation for the combined crfuical stress,

-27-

Since Over! /' O.8oy ,the reduction for the inelastic range

sl?plies. as follows ~

: ~vc~ :: 34.9(1'- 0.16 j~:§)= 29.~ ksi

Since aver:: JaJ.+3n;21

:; 0.05'22Pcr , Pcr = 29.8/0.05'22, or

Per = 570 kips

In Table 1.8 and 1.9 are surrnnarized the. or! tical stresses

and lo~ds for ·all girders., The bend1ngand shear groups

never exceed the elastic limit and thus 0cr1 = ocr and

~cri = ~cr. The eente~ panel of E5-Tl was sUbjec~ed to pure

moment and therefore no' entries are made' under the' qolumns

for shear.

-28-

1.7 Deflections

In order to check on the elastic behavior of the

girders, their predicted deflections are evaluated in this

section. Again three groups exist': bending, shear, and

combined loading girders. The centerline deflections are

obtained for the bending and combined groups while the end

deflections are given for the shear girders.

The method of Virtual Work is used to obtain all

deflections. In this method a unit load is applied to

the girder at the point where the deflection is desired

origin of the x-axis is taken at the end of each girder.

integrals extend over the entire girder length where the

In this expression M and V are the moment and shear due to

J~ dx + J Vv dxEI GAw

v =

computed as the sum of the bending and shear contributions:

the actual loading, E = 30,000 ksi is the modulus of elas­

ticity, and G = 11,530 ksi is the shearing modulus. All

and its resulting moment, m, and shear, v, diagrams drawn.

Then the deflection directly under this "dummy" load is

-29-

The units for all quantities and dimensions are kips and

inches.

To illustrate the procedure followed in calculating

deflections, the expression for the centerline deflections

of the bending girders is developed now. In the example

shown on the next page, the loading is first pictured, to­

gether with sketches of the areas and moments of inertia of

the girders. Then the moment and shear diagrams, both for

the real and dummy loadings, are drawn. Below these diagrams,

the integrals are written, the first three representing the

moment component and the last one inclUding the shear con­

tribution. Observing the symmetry of the loading and cross

sectional properties, the integrals need only be evaluated

over half the length of the girder and then doubled to obtain

the final value.

SUbstituting the properties of GI-Tl into the resulting

equation (a), where Ie' I m, and Ae equal 15,550 in4 ,

14,380 in4 , and 19.10 in2 respectively, the centerline

deflection for the applied load of cP = 100 kips would be

1.172 inches. In this case the shear component i85.8% of

the total deflection.

Using the same procedure as above, the equations needed

to evaluate all required deflections are obtained. These

expressions are listed on page 31 together with the cases to

which they apply.

-30-

C~nterllne Deflection Qf'Bend1ng"Girde~~

V-diagram

v~.diagram.

Loading

m~diagram

Mom~ of" Inertia

M-diagram.

k " p p , "

,"150-, 'w~ , '33J~~~ ~~

540"

AeA,rn

Ie 1m

r~~ llSOP /~~~

+P .. '

+1/2 . 11

V~ - J: dx +.. J~~w dx .

150 . 183·'·. :::: 2 J<PX) (xL2)dX + J(150P) (xL2) dx

EIe . < EIeo " 150 . .

270'·" 150'

+ J(150~i(x!2) dx + r<Pl~~!2)183 . m... ~

= 2xl0.3 [562.~P + 412.1P + 1418p + O.0750Pj. EIe·· EI EI·' Aw'G,6 m .

, ;

. Vt = p[64.97/Ie.+ 98. 53/Iiri+ O.OI301/Ae] (a)

-31-

All bending girders, ~xcept Gl)" were reinforced with

ste~l ~lates "afte~ their first test. With a new cross

B~oti,on' 'pre,sent, . whose moment of inerti'a I 'is' 'listed in

th.~: "sp'eclal s<?ct'i.ons" of· Table 1.6 the expres~ion for the

centerline deflection,in the second test is:

Vet = P(64.97/Ie.·+ 54.~3/Im + 43.59!I + O.01301/Ae ) (b)

The shear girders have a maximum deflection at their

ends. Obse'rving t,p-at the'sa girders ,bav-6 cover plates at

their reaction points " thus having' specia.l moments of

inertia I, the equation 'for' end deflections is:

Va = P(5.689/Ie + 7.316/Im + 25.39/1 + O.0132/Ae,

+.O.0075/Am) (0)

Girder El, the first of the girder,s' under combined

loading,had its second cover plates term~nated 75 inches

frol11; 1 ts ends. ' ·Let~ing the moments' of ~nert1a of the

se,ction wi th and without the second cover plates be Im and

I, the relation for centerline deflect~oh is:

All other girders. under combined loading had constant

cross sections throughout their lengths. As such, the

centerline" deflection's can be found ,from Eq. (d) by sub­

stituting I = lrn.' The resultin'g e'quation is:

Vt = P(22.23/Im + O.00689/Aw)

A summary of girde:r def~ections, co~puted from the

above equations,' ,is given in Table 1.1011 Here, the bending, .

and shear componen'ts o;r the total deflection are listed,

together with the equation that is applied to determine

( d)

(e)

them. The centerline deflection ·18 given for the bending

and combined groups while the end deflection is' listed for

the shear girders. As ~ m~tter of interest, the percentage

of the shear contribution to the total deflection is in­

cluded. All deflections are eva~uated for ~ = 100 kips.

, --33-. I

Table 1.1'- summa~y o~ .. ~G:t:rder Pa,rameters

beH ~Q).' . tM

'rrj .' ."0H. .. 'g;t

.,....,., 0,o 'H

.'. '1,

S ....:: ~~tI) -n .. "d ',",rn 4-). "':~ tJio 0, t) ~Q) 01~ .Q) Q)" rl (I)

t.,) rJ)" :;: tf) .f=I .

stiffener Location· of ·Failure ~" Spacing: C1 . 'arid Reinforcements'.Tl· " ,T2'· Tl ' " 'T2T3 T4'," T3 " .,T4

Gl I. 185 .,1.50' 0.75 .CrCJ r::r:cJG2

,bO ·.'II 185 1.50 0.75 ITO crrJ~.1'4ro

G3',$:I .

III 185 1'.5° 0.75 rrr:::J m=J(J)

~

G4 <DII 388 1.50 0.7,5 ITO r:tDH

~,

P-t

05 I·II 388 1.,,50 0.75 ITCJ ITO

'1.50' 0.75 ~J !ZIJII]G6 I'I 259 .

I.

H 0.50 ~ai ',I ~ I I,

<D,dCIl ~ ITJZJ [Z[]S]G7 ,'II' 255 1.00 1.00

Table 1.2

Summary of Or-css ,Sectional 'Dimensions'in inches

Top Flange Bottom Flange Web ThiqknessGir- 'Cross Width 'Thick- 'Width Th1ck- Test End·dar· ' Sect.• ness, ness

20 d 2c d t' t

Gl-" I 20.56 0·427 12.25 0.760 0.270 0 .. 38,2

G2 II 12.,19 0.769 12.19 ,0.774 0.,270 0.507

G3 III 8.62 0,.328 12.19 0.770 0.270 0·492

G4 II 12.16 0··-774 12.19 0.765 0.129 . O. 392

G5 III' 8.62 0.328 12.25 0.• 767 0.,129 0.392

G6 II 12.13 0.778 12.13 0.778 O.I?3 0.)69

G7 II 12.19 0.769 12.19 0'.766 0.196 o. 38'1

El IV 20.56 0.427 12.25 . ',' 0.760' 0 •. 382'- .:

E2 V 12.i9 0.769 ' 12.19 '0.774 o~'507

E4 VI 12.16 0.,774 12.19 0.765 0.392

E5 III. 8.62 0.328 12.25 0.767 0.392

G8 II 12.00 0.752 ',12.00 0.747. 0.197

G9 II 12.00 0.755 12.00 0.745 o.i31

'{'PL A: 15.04 x 0.882,Cover Pl'ates

PL B: 18.00 x 0.750,

PL c: 16.00 x 1.007

PL D: 11.19 x 0.510

"

TABLE 1.3

Summary of r-1a.terial Properties (Gl to G7) .

Des i g nat ion Che~ica1 Analysis Mill Tests Fritz Lab. Tests

LocationThick-

CouponSpecif'i- Heat Slab C Mh P S CJy _ (Jult El~ng CJyst o-ult Elong Ared 0;

ness cation No. No. % ::t % " % ,(ksi) (ks i) 15/ (ksi) (ksi) % % (ksi)..r~ /0,.

B attorn Gl CP 9 40572 -., . 40.2 65.8 30.0 35.8 61.8 33.5 '63.9 127.9_

Top G2 CP 17 40569 42·0 66.4 29.0 38.6 63.7 27.1 61'.9 120.7([) Top G4 OF 27 r-I 40511 40.5 66.4 30.0 37.6 63.8 31.5 60.9 125.3r-co B attom G3 3/4n OF 40 C\I 40569 .17 .70 .016 .026 42.0 - 66.4 29.0 38.1 63.7 32.1 61.1 125.9

G5 . c'p 51 ~ 40570 40·4 65.1 30.0 '37.0 63.0 "32.6 61 . .5 123.3B attorn ....0

~ Top G6 CF 54 0::> 40561' h1.9 66 .. 0 30.0 37.9" 63.8 31.4- .59.0 121.4cd Top G7 Op 62 -.. 40568 41.7 65.8 29.0 37.0 63 .. 1 31.6 . 59.6 '122.3

M ~

fx.t Top Gl 7/16:T CF 7 >-I 87K270 40833 .22 .59 .011 .029 40.8 66.5 29.0 3.5.2 6~ .5 28.2 59.4 -Top Gl CF 8 "r""I 35.5 62.2 30.0 58.-1 -

0)

~

Top Cov. G6 1/2" CF 53 0 87K254 ,(4°859) .22 .59' .008 .023 38.1 63.2 29.0 33.6 60.8 29.3 61.5 129.2Top Cov. G7 CP 63 E-t . 33.3 60.1 31~e 62.4 -....0 0

G2 CP 12 'U'\ ...::t 40671 40.5 66.3 29.0 35.4 63.2 29.9 59.4~ I. -0 G2 1/2 fT CP 12A CV'\ ~ 4067l 40.5 66.3 29.0 34·3 62.7 24.0. 51.6 -...-i r- ed~ G3 OP 35 ('1"'\ 0 41200 40.2 67.8 26.0 37.3 67.4 2E.7 60 .. 0 137.00 "d r- .22 .59 .Oll .029Q) ~

~{\J

t1 G1 OF 2 E-i ~ 39809 40.9 67.7 28.0 41 69.2 24·9 51.4 -rt.1 ..-f r-'"0 Gl 3/8" CP 2A « ctS co 39809 40.9 67.7 28.0 42·4 68.4 21.8 32.0' -~~ G4 OF 22

'0'" 398.08 42.,0 67.6 29.0 40.0 67.0 28.2 63.3 105.6'Q)

G1 CP "3 .I"'i 32.9 55.8 35.1 62.2~ -.D' G1 1/4,i CP~ 3A ..,..; 84K24l > 53268 .13 ,.49 .009 .026 39.1 60.9 28.0 33.0 54.4 34·6 58.2 . -"dtD G2 CF 13 0 35.3 60.0 31.1 63.3 -

Q :E:~ 0

G6 OF 57 ...-40.7 64.5 23.5 62.4 28.6 53.5 112.0...-i -

~ G6 3/16" OF 57A 59K346 83483 .22 .50 .008 .020 40.7 64.5 23.5 36.8~ 63.3 30.0 49.3 108.2. 0Q) G7 CP 66 40.8 66.3 24.5 - 36.6 64.2 28.4 52.7 113.4et.l

~ G:4 CF 23 40.6 62.9 28.5 43.5 60.7 28·4 .51.4 104.7tr.ICD G4

1/8 l1OF 236 ASTM-A 40.6 62.9 28.5 43.2 60.9 25.4 63.3 -133.38 GS CP 47 245-57T 9%198 - .18 .82 .010 ~022 40.2, 62.3 26.0 46.6 62.'8 27.1 59.9 129.9

G5 CP 47B 40.2 62.3 26.0 44 .. 8 63.5 24.2 ,57.9 126.8-

r-f 8" pipe G3 O.322 n CF 3i A-53 - - - - .017 - 40.2 60.4 42.5 35.5' (,51.5)Jii Grada.p!- - - -~

Note: A ref'ers to call,pon taken in transv~rse dir~ction.

B refers to additional coup-on taken next to the original one, e. g., qP 23 and GP 238

IW\Jl..

I

"

...::.'.

TAB IE .. 1.4

Summary of -Material Properties (continued)

Des i g nat i' 0 n Chemical Analysis Mill Tests Fritz Lab. Tests. ~

Thick- Speciri- Heat Slab C Mn P S0:.

(j'ult Elong O"'yst O'~lt Elong Ared (JryLocation ness Coupon cation No. .No. % % % d1 ksi ks1 % ksi ksi % % ksi/0

Top Cov. E2 CP E5 - 60.7 32.2 61.5 122.6Top COV. E2 1" CP E5B p.., -1772 .17 .65 .010 .032. 38.5 62.3 28.0 28..6 60.9_ 31.6 61~9 119.3Bot.Cov. E2 CP E6 30.3 62.0· 30.3 60.4 119.8>tTou COV. El CP El ..,.; r-i 30.1 59-.8 31.9- 64.2 125.3Ul C""\

Q) Top- Cov. El 7/8" CP_E2 ~ i--i 1773 .17 .64 .008 .032 38_.7 62.8 29.0 30.2 60.2 32.2 62.6 121.1~w Top Coy. El CF. E2B

~co 30~1 60.8 33.4 62.5 120.4r--

s:l C"'"\O

Bot.Cov. El CP E3r-....::t

61.5 57.9as- f'I'\" - 31.0 113.2Bot.Cov. E1 CF E.3B +t

1771 .16 .65 .011 .031 38.7 63.0 29.0 29.6 60.9 32.0 62.1 119.7r-i < aslit Bot.Cov. El CP E4 :z."'C 30.0 62.2 30.2 60.0 121.6

3/4ft E-I CD •(/) E

Top G8 CPEG3<C .....

C'l""\ U\ 40.2 76.1 27.0 . 49.3 123.1asTop G8 CPEG4 0' r-f 42.4 76.7 24.5 53.7 132.2.... r-i -~ 45.1 75.5Top G9 .GP EG9 -0 ~ .26 -70 .022 .027 22.0 42.1 76.3 22.6 53.5 131.2co 0'Top ;_ G9 CP EGIO CD 41.5 76.6- 25.9 51.5 128.8 'n...... r- eo

It-I t"f"\-.....

(\J--0- '"G8 CP EGI 0 C"'\ r-f . 37.9 57.8 28.1. 58.4 -:E: t"'"\~G8 3/16 lf CP EGiA ~ .13 .52 .008 .028 39'.5 56.7 32.0 38·4 58.0 28.8 42.2 -en 0'

.0 .. G8 CP EG2 " r- a:> 38.4 57.4 29·4 62.3 -C"'\(D 8

G9- CP EG7 - roo-=:t ,l.-::j- 43.8 58.0 23.1 48.8 -;;: U\

G9 CP EG7A -:E: fa> C'l""\ ON . 42.6 '-57.1 21.7 47.2 -1/8" E-il.r\~ C"'\ 1.J\~._ ,.18 '-49 ,.-011 .0}2 39.6 56.7 29.0~

G9 . CP EGB rJ]~ cd ~ I 0' - 47.5 59.2 25.0 45.1 -<C\I H -::t ~("\'"\ .G9 CP EG8A _<0 0' 44.1 59.2 27.3 47.4 ---

Note: A refers to coupon tak~n -m transverse direct-ion

B re:rers to- ~<ldit1onal~oupontakeIl:-next to the -original one~ e-.g., CP E2 and_ CP E23

'"

IW0'I

Table 1.5

Summary of Static Yield stresses(kips per a'quare' inoh, ks1)

Girder Cr9ss B'langes WebsSect. To.p 'Bc)ttom T~st End

Gl I 35.4 35.8 ' 33.0 41.7

G2 I'I 38.6 37.6 35.3 34·9

G3 III 35.5 38.1 33.7 37.3.. G4 II 37.6 37.0 43·4 40.0

a5 III 35.5 37.0 r~5 9 7 40.0

G6

G7

II

II

37.9

37.6

36.7

36.7

El IV 35.4 35 .. 8 41.7

E2 V 38.6 37.6 34-9

E4 VI 37.6 37.0 40.0

E5 III 35.5 37.0 40.0

G8 II 41.3 41.3 38.2

G9 II 41.8 41.8 44·5

, {PL A: 30.1.,Cover Plates

PL B': 29.8,

PL c: 29.4

PL D: 33.5

, - .38~

Table 1.6'

'SUmmary. , .

Mo'ciuliof M9m~nts of Inertia "and Se'c.tion, '

,EQd $p~~ .•T. e ,s. 't, S e c t 1 0 n sect." Sect.

G;l.rder : '1m Sa " Sb ':Ie ' 'I. 1'n+ in) . ,in3 1n4 .in+

"

Gl 14,3'80 . 555 568 15,,550 12 210,

G2 14,940 578 581 17,400 16,170

G3 16,220 488 620 ,~8~530 17,'790"

. G4", 13,4,20 522 519 16,160 14, 6~.,O

G5 14,710 443 561 17,450 16,9$0

Gl?, G7

14,,180

14,,100

550$48 ,

550

'547

'16,010

16,030

23,750

23,.7'60

El 52,920 1,922 1,968 33,·6,70

E2 39,620 1,480 . 1,485

E4 '34,390 1,.292 1,28.7..__....

E5 17,480 $24 .' 672 "-"",,--G8 i3,640 531. 528

G9 12., 960 505' 501

..

-39-

. Tab'le 1 ..7

,Summary of Reference, Moment~ and Loads

Girder Test . M'f , My Mp , !?y l'pk-1n' k-in k-ln kips kips

Tl 15,700 19,600 ,21,900 1)1 148Gl

T2 1Q,400 15,100 18,700 ~Ol' , 118

G2 Tl,T2 '18,400 22,300 .' 24,200 149 167

G3 T~,T2 16',600 17,300 23,600 116 156

G4 Tl,T2 ' 18,000 19,600 '21, 200 130 139

G5 Tl,T2 16,500 15, '700 21,3'00 105 134

G6 Tl,T2,T3 18:,200 20,800 '2'2,600 193 205

G7 Tl,T2 17,900 20,600 22,300 196 208

Tl,T2',T4 .5'~, 000 60,000 ' 68, 600, 826 ,920El

T3 36,600 40 ,,700 47,100 905 920

E2 ~1,T2 43,400 48 ,$00 54, 1,00 716 855

Tl 880 905

E4 T2 '39,100 43,000 48,600 658 691

T3 639 666

Tl 248 367E5 16,500 18,600 27,500

T2 ..... 358 386

.Tl, T3, T4 280 368a8 18,900 21,900 23,600

T2 410 434

Tl,T3, 19,206

264 354G9 21,100 22,700

T2 324 336

Table 1.8

Summary Q·f Critical stress'as and Loads

. Bending Girders

Girder Test. on ~ k O'er Perksi kips

Tl 1'.50 23.9 ,18.7 70.1G1' 185

18.'6T2 0.75 14,.5 41.,9

Tl 1.50·G2 185 23 .. 9 18.7 74·1 .

, T2 0.75

Tl 1.50G3 185 23.9 18.7 82.1

T2 0.75

TI' 1.50G4 388 23.9" 4·25 15.3 0

T2 0.75

Tl 1.$0,G5 388 23.9 4,·,25' 17.0

T2 0.75

Shear Girders

Girder Te,st a (3 ,k 't" c'r Per

Tl ° 1.50 7.12 2.84 27.4

G6 T2 . ,0,.75 259 13.5 5.38 51.9

T3 0.50 2,5·4 10.1 97.6

Tl 1.00G7 255 9.34 '3.84 37.6

T2 1.00

Table 1.9

Summary of Critical Stresses and Loads

Girders under Combined Loadin,g

Ben~ing . Shear I CombinedGirder Test ~ (3 I k O'cri k (Jeri, .o-vcri .<rver I Per

ksi ks i 1 ksi ks-i kips

Tl 3.00 5.19 9.01 18.0 . 18.0 332T2 1.50 7.12 11.1 21.8- 21.8 402

El T3 1.50 ·131" 23.9 37.2 7 .12 l·l~ 1 20.3 20.3 415T4 1.00 9.34 14.6 27.4 27.4 S06

Tl 3.0065.2

5.79 15.8 37.5 29.8 570E2 T2 1.59 99 23.9 " 7 .12 19.4- 44.1 --JO.4 584 1

+:-.....Tl _.1.50 7'.12 11.6 21~3 21.3 445 1

~4 "T2 '0.75 128 -23.9' 39-.0 13.5 22.• 0 38.5' ' 33.4 513T3, 0.50 25.4 41.4- 46.9 34.5· 517

E5 Tl 0.36128 -- 39'.0 ·33.-4 - 314

'T2 ,0.75 23.9 39.0 13.5 22.0 38.-.8 33.4 322

Tl 3.00 5.79 2.40 5.99 5'.99 41.5T'2 1:..50

2547.12 2.96 5.59 5.59 56.4

G8 T3 ~.50 - 2).9 .9.91 .. 7.12 2.96 6.96 6.96 48'.3·T4 . . l~OO 9.34 3.88 8.26 ~.26' - 57.3

Tl 3.00 5·.79 1.06 ,2.32 . ·2.32 12.·9G9 '1'2 1.50 382 -23.9 .. 4-.38- 7.12 '1'.31 2.36 2.36 - 16.8

T3' 1.50 7."12 1.31 ' 2.78 2.__18 15-.5

. -42- .

Table 1.10

Summary of GirdC?r Deflect,ionskips)'(in inches and under nominal· lo~d P=lOO

Eq•. Deflections due to %ShearGirder ~est Used Bending Shear Total o Total

Tl (a) 1.1,°4 1.172 5.·8,Gl 0.068

T2 (a) 1.225 1.293 5. .3

Tl (al 1.033 1.,084 4.7G2 0.051

. T2 (b) 1.008 ,1.059 4.8

Tl ,(a) 0.958 '1.011 5.2G3 0,. 053

T2 (b) 0.931 .0.984 5-4

T'l (a) 1.136 1.202 5.5,G4 0.066

T2 (b.) 1.102 '1.168 5.6

Tl (a) 1.042 ,1.108 6.0G$ 0.066

T2 (b) 1.000 1.066 6.2

a6, All (cl 0.194 0.150 0.'344 43.6

G7 All (c ). 0.194 0.147 0.341 43.i

El (d) 0.045 0.034 0.079 43~1

E2 0) (e) 0.056 0.026 l 0.082 31,.7..J..)

E4 ta (e) O.O~4 0.033 , 0.097 34·0(1)E-i

E5 r-I ( e,) .0.127 0.033 0.160 20.6r-f

G8<

28 .. 8(e) 0.163 0.066 0.229

G9 .( e) 0.172 0.099 0.271 ·36.5

IO:'~3'-9'1-6'-3"+- 6'-3'~3~* Id-O'~~6"I.. - - - 40'-Cf' - J

. . j . . 1, 1

,---­4~2U i-*-- :r;---~~.........L~~U-il

~ Test 1! Section

I y+

6h-jt= 12'-6,,-J 3'-9"~ 6·-3,l6~3·J3~9,L 12'-6'Y~6"t-- - , 45·-0"-----~

SHEARJVI

+--- v=-p

V= P

SHEAR, VI

v=-p

MOMENT,MJ - .

h Mmolt.=P·150"

MOMENT,MI

~ JI

~-Mmax:=P-120

-Fig. l.l~ Test Setup of Bend-ing Girders Fig. I. 2;: Te-st Setup or Shear Girders'

III J. b=5o"

Jd~2CP-

'p

~1 Iat= I !.~~t=12~S~.. -~.~-S" i2'-"6"==:jI-SII ... .. 26':-6"' ' ..

r-2c -j.df ~f-

b=50" ) I

L:.-d-r-

-.!2C 1-

-j 2c Gd

_

1jtlill 1:"~2C~

0.328 --L8'~8a

tl--- -. .

V=O.5P;. Gt G2,G4

G6 J G7.G8~G9

G3,G~

·E5

SHEAR,VI

'V:-O.5P

F"ig. l.>~ Test St?tup o:f G~iptl·erEf':·'Under

VI. I b=50"

---1..E.A

E4

F1ig o 1.Lr' Gi~der Cross Sections

ftAItS ~c

tlf t

b=50" IV V b=50"

LMmax_=P·7SH L ~.A1

-l12.8

-c IlCEI £2

MOMENT,M"I

Cornl:;lnec1 IJ{)ading

Thickness

Thickness

Width

0.431 OA31 0.430 0.425. O~425 O~424

[~ C~7~] ~~i:~2%'6 .[W>i2~?~??@:I.0.432 OA32 Q430 . 0.4230.423 0.422

20.5620456 20~56 20.56 20.56 20.56,

Girder GI

Average

0.427

0.427

2056 in

0.427 in

0.253

0.264enU1Q)

50c:~ 04268:c1-

0.274

0.277

· 0.257 0.259 • ·

·~I

• O~267 0.271 . ·

· • 0.271 Test WebO~275 •

JtSOxlj4

.rzz: w 0.274 (' 0.277 1Z2 U ????? ??22ZiJ-

CP3

~'CP4

· • 0.277 0.278 · ·

0~259 0.257

,O~270 O~268

O~274 O~272 r O.270in

O~277 0.276

0.278 0.276

'....

(AU dimensions are in inches)

~ ,

Thickness Q760 0759 0759 O~762 0762 0.761

I~ G~9 ~] ~o,t~~";~~,ongel~??c~io?@]Thickness 0.760 '0759 0758 0.761 0762 04761

Width 1225 1225 1225 12.25 1225 1~25

Fig 0 105 .. EVA.LUAT'ION OF PLATE DIMENSIONS AND COUPON LOCATIONS

0760}0.760 in

0476012425 in

Subject: Coupon Dimensions and Test Results

Specimen No: GP 27 IDate: July 5,1958

Note: Crosshend Spep.d 0.10 inches/minutel Tested by: STY, 80.

/" J_~Il

1

Thickness

0.769

0.770

0.767

0.769

0.768

0.769

0.768

0.7700.771

Width

1.500

1.500

1.500

1.500

1.500

1.500

1.499

1.499

1.499

Upper '(.F,> •••••• 48,60Qlb

Lower Y. F! '.' • • • •46,OOOIb

46,250 }Dynamic'f.F? 46,250 46,2001b

46.5-45.8

Static Y. P. :~:~~~ }43,4001b

Ult. Lood • • · • . • • 73,500lb

Rupture Load •••• ,56,4001b

Reduced Area . ~ . ~..• O.450j~

Elong. Gage Length. ',' 10,49 in

5"

Area 0.768 '1.50=1.152 in2

Static Yield Stress

Ultimate Stress

Elongation

Rupture 'Stress

~ - 43.4 37. 6 k ·y-~-: • SI

(j, - ~- 638k 'u - 1.152 - · S I

E= I0.4~9~98'IOO=31.5%

Fig. 106 - TYPICAL DATA SHEET FOR COUPON TESTS

Teat No., CP..2t Slze U50.0~~t(.Q\7.fi.I~Area l.leiZ.ti: ~.Yield Point Lbe. Sq. ID•......~f&.OQ •••.•.•U1tlm8te Str_LbL Sq_ In 6~............ •

I Elofll1ation l .. II .,-=:1' '!Iltt ~O.9°j' .tllIy'" ~ I:IlTV f.~ r rIn.....1.9.B.•,..Inchea.,........"".,f),,........Per CelJt. EloDlllldoll.......'......" ..Per Cent. Reduced Area...,..~........"Il....Date....K_••,,""...M .....'.... ,

:n\C.

en.....

"" ::0!?:

-t z-<"'Un· c:~ 2_.....V'l II-+

0....CD 0&It..,. 0I

~Vl-+ 3-..,~. "::s s-OI::..,<CD

Average Thickness = 0.323 in.

Average Diameter : 842 in.

Cross Sect- Area, A = 8.56 in2

Yield Load Py ;:: 300 kips

Yield Stress ay = 35.5k.s.i.

€=~h ~=~A

0.3100.32"3

-tp

8or i 1 [ . I I I I iii iIi i •

0.5 1.0 15in €li" i j iii iii i I I I I iii i •o 10 20 30 40 50 60 ~~·lo3

10

01

o due to loCOI

J .. jP,to

zoor! i .~2~ I j

o

100 .I

30

4

Fig. 1.8 - YIELD STRESS DETERMINATION OF TUBULAR F-LANGE